Free Printable AP Calculus BC Review Sheet

1.

Equals

a)

_a∫^cf(x)dx

b)

_a∫^bf(x)dx

c)

_b∫^cf(x)dx

d)

_c∫^af(x)dx

2.

Equals

a)

∫ f(x)dx

b)

cx∫ f(x)dx

c)

c∫f(x)dx

d)

(1/c)∫f(x)dx

3.

equals

a)

f(x)

b)

f(x) + C

c)

f '(x)

d)

f '(x) +C

4.

a)

Intermediate Value Theorem

b)

Rolle's Theorem

c)

Average Rate of Change

d)

Average Value of f

5.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

6.

Equals

a)

_d∫^cf(x)dx

b)

- _d∫^cf(x)dx

c)

f(d) - f(c)

d)

f(c) - f(d)

7.

a)

f '(g'(x))

b)

f '(x)g'(x)

c)

f '(g(x))g'(x)

d)

f '(g(x)

8.

a)

Volume using Washers

b)

Volume using Disks

c)

Volume using Shells

d)

Volume using Cross Sections

9.

a)

f(x)

b)

f(x) + C

c)

f '(x)

d)

f '(x) + C

10.

a)

c⋅f(x)

b)

c⋅f '(x)

c)

c⋅f '(x) + c⋅f(x)

d)

c⋅f '(x) - c⋅f(x)

11.

a)

Volume using Disks

b)

Volume using Washers

c)

Volume using Shells

d)

Volume using Cross-Sections

12.

a)

position

b)

acceleration

c)

total distance

d)

displacement

13.

a)

f '(x)

b)

0

c)

∞

d)

f(x)

14.

a)

f(u)

b)

f(u) + C

c)

f(u)⋅(du/dx)

d)

f(t)

15.

a)

f(a) - f(b)

b)

f(b) - f(a)

c)

f '(b) - f '(a)

d)

f '(a) - f '(b)

16.

a)

linear approximation

b)

integration by parts

c)

average rate of change

d)

product rule

17.

a)

Mean value theorem

b)

Rolle's theorem

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

18.

a)

(1/n)⋅u^n-1(du/dx)

b)

n⋅uⁿ⁺¹(du/dx)

c)

n⋅u^n-1(du/dx)

d)

(1/n)⋅uⁿ⁺¹(du/dx)

19.

a)

(1/n) ⋅x^n-1

b)

(1/n) ⋅xⁿ⁺¹

c)

n ⋅x^n-1

d)

n ⋅xⁿ⁺¹

20.

a)

f '(x)⋅g(x) + f(x)⋅g'(x)

b)

f '(x)⋅g(x) - f(x)⋅g'(x)

c)

[f '(x)⋅g(x) + f(x)⋅g'(x)] / [g(x)]²

d)

[f '(x)⋅g(x) - f(x)⋅g'(x)] / [g(x)]²

21.

If y = f(x)/g(x), then dy/dx =

a)

f '(x)⋅g(x) + f(x)⋅g'(x)

b)

f '(x)⋅g(x) - f(x)⋅g'(x)

c)

[f '(x)⋅g(x) + f(x)⋅g'(x)] / [g(x)]²

d)

[f '(x)⋅g(x) - f(x)⋅g'(x)] / [g(x)]²

22.

a)

speed

b)

acceleration

c)

displacement

d)

total distance

23.

a)

Volume using Shells

b)

Volume using Disks

c)

Volume using Washers

d)

Volume using Cross Sections

24.

Find the limit of the function as x approaches 2.

(Click the image.)

a)

1

b)

-1

c)

5

d)

DNE

25.

Find the mistake if possible. (Click the image.)

a)

The Diff EQ is solved correctly

b)

Step 1 is incorrect. The separation of variables wasn't done correctly.

c)

Step 2 is incorrect. They didn't integrate x² correctly.

d)

Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

26.

Solve the Initial Value Problem

a)

$y=-\frac{1}{x}$

b)

$y=-x^2$

c)

$y=\frac{-1}{x+1}$

d)

$y=\frac{1}{x+1}$

27.

Select the integral that would find the volume of the region revolving around the given axis.

(Click the image.)

a)

b)

c)

d)

28.

a)

A

b)

B

c)

C

d)

D

29.

a)

position

b)

acceleration

c)

total distance

d)

speed

30.

a)

A

b)

B

c)

C

d)

D

31.

Find the limit

a)

0

b)

8

c)

16

d)

Does Not Exist (DNE)

32.

Find the Limit

a)

0

b)

-1/4

c)

-5/4

d)

1

e)

DNE

33.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

34.

Find the limit as x approaches 1

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

35.

Select all statements that are TRUE.

a)

b)

c)

d)

e)

36.

Determine the Limit at Infinity

a)

0

b)

-1

c)

-5/2

d)

DNE

e)

infinity

37.

Find the limit at infinity

a)

0

b)

infinity

c)

4/3

d)

-3/2

e)

DNE

38.

Find the limit at infinity

a)

0

b)

1

c)

infinity

d)

DNE

39.

Which of the following statement(s) are false?

a)

f is continuous at a

b)

the limit as x approaches a exists

c)

f is differentiable at a

d)

f(a) exists

e)

None, all statements are true

40.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

41.

a)

A

b)

B

c)

C

d)

D

e)

E

42.

a)

A

b)

B

c)

C

d)

D

e)

E

43.

a)

A

b)

B

c)

C

d)

D

e)

E

44.

a)

A

b)

B

c)

C

d)

D

e)

E

45.

a)

A

b)

B

c)

C

d)

D

e)

E

46.

a)

A

b)

B

c)

C

d)

D

e)

E

47.

a)

A

b)

B

c)

C

d)

D

e)

E

48.

a)

A

b)

B

c)

C

d)

D

e)

E

49.

a)

A

b)

B

c)

C

d)

D

e)

E

50.

The graph of f has a relative extrema when f'

a)

changes sign

b)

equals zero

c)

goes from negative to positive

d)

goes from positive to negative

51.

Let $g\left(x\right)=\int_0^xf\left(t\right)dt$ , where the graph of f is shown above. On what interval(s) is g decreasing?

a)

[2,8]

b)

[0,5]

c)

[2,5]

d)

[-5,-2]U[0,5]

52.

If $w\left(x\right)=f\left(x\right)q\left(x\right)$ , then $w'\left(x\right)=$

a)

$f'\left(x\right)q'\left(x\right)$

b)

$f'\left(x\right)q'\left(x\right)+f\left(x\right)q\left(x\right)$

c)

$f'\left(q\left(x\right)\right)q'\left(x\right)$

d)

$f'\left(x\right)q\left(x\right)+f\left(x\right)q'\left(x\right)$

53.

For the function f, it is known that $\lim_{x\rightarrow-1^-}f'\left(x\right)=\lim_{x\rightarrow-1^+}f'\left(x\right)$ . Which of the following must be true?

I. f is continuous at x = -1

II. f is differentiable at x = -1

a)

Both I and II

b)

I only

c)

II only

d)

Neither I or II

54.

Evaluate $\lim_{x\rightarrow\frac{\pi}{4}}\frac{\cos x-\cos\left(\frac{\pi}{4}\right)}{x-\frac{\pi}{4}}$

a)

$-\frac{\sqrt{2}}{2}$

b)

DNE

c)

$0$

d)

$\frac{\sqrt{2}}{2}$

55.

$\frac{d}{dx}\left(\frac{1}{1-2x}\right)$ equals

a)

$-\frac{2}{\left(1-2x\right)^2}$

b)

$-2\ln\left|1-2x\right|$

c)

$\frac{2}{\left(1-2x\right)^2}$

d)

$-\frac{1}{2}\ln\left|1-2x\right|$

56.

For a particle moving along the x-axis, the particle's speed equals 2 when

a)

$\left|v\left(t\right)\right|=2$

b)

$v\left(t\right)=2$

c)

$a\left(t\right)=2$

d)

$\left|a\left(t\right)\right|=2$

57.

If $f\left(x\right)=\int_4^x\left(\cos\left(2t\right)+3\right)dt$ , then $f'\left(x\right)=$

a)

$\frac{1}{2}\sin\left(2x\right)+3x$

b)

$\cos\left(2x\right)$

c)

$2\cos\left(2x\right)+3$

d)

$\cos\left(2x\right)+3$

58.

The region R is the area enclosed by the functions $y=2x$ and $y=x^2$ . Which expression represents the area of R?

a)

$\int_0^2\left(x^2-2x\right)dx$

b)

$\int_0^2\left(2x-x^2\right)dx$

c)

$\int_0^4\left(2x-x^2\right)dx$

d)

$\int_0^4\left(x^2-2x\right)dx$

59.

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

v = 0

b)

v = 1

c)

v = -1

d)

v = -2

60.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

61.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

a)

2

b)

4

c)

6

d)

8

62.

v (t) > 0 means

a)

the particle is moving to the right

b)

the particle is speeding up

c)

the particle has positive position

d)

the particle is at rest

63.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

64.

Which of the following can be used to determine when a particle is at rest?

a)

x(t)=0

b)

v(t)=0

c)

a(t)=0

65.

Which is true for the graph of velocity of an object?

a)

The object is speeding up for parts A, B, and C

b)

The object is speeding up in parts D and E

c)

The object is speeding up in parts A and D.

d)

The object is stopped or at rest in part B

66.

What does a flat (horizontal) line on a velocity-time graph mean?

[Example section B on this graph]

a)

The object is not moving.

b)

The object is moving, but at a constant velocity.

c)

The object is accelerating, and its acceleration is positive.

d)

The object is accelerating, and its acceleration is negative.

67.

You can calculate the slope of a velocity-time graph.

If you calculate the slope of the graph between two points, what would that tell you?

a)

The velocity of the object.

b)

The distance travelled by the object.

c)

The acceleration of the object.

d)

The mass of the object

68.

Besides v(t) = 0, what else is needed to know an object changes directions at a specific time, t ?

a)

v(t) = 0 and a(t) = 0

b)

v(t)=0 and velocity changes sign

c)

v(t) = 0 and acceleration changes sign

69.

Part E of the graph is from 95s to 105s. Which of these statements is true about Part E?

a)

The object is at rest.

b)

The object is slowing down

c)

The object is speeding up.

d)

The object has negative acceleration.

70.

What is the total displacement of the object represented in this position/time graph?

a)

0 meters

b)

100 meters

c)

140 meters

d)

200 meters

71.

The intermediate value theorem (IVT) is primarily concerned with which of the following?

a)

y-values

b)

first derivative values

c)

second derivative values

d)

x-values

72.

Which of these is NOT a hypothesis of the Mean Value Theorem (MVT)?

a)

A closed interval

b)

A differentiable function

c)

A continuous function

d)

A twice-differentiable function

73.

Tangent line formula.

a)

$y-f\left(x_1\right)=f'\left(x_1\right)\left(x-x_1\right)$

b)

$y=f'\left(x_1\right)\left(x-x_1\right)$

c)

$y-f\left(y_1\right)=f'\left(x_1\right)\left(x-x_1\right)$

d)

$y=f\left(x_1\right)\left(x-x_1\right)$

74.

The fundamental theorem of calculus.

a)

$\int_a^bf\left(x\right)=F\left(b\right)-F\left(a\right)\$ where F is the antiderivative

b)

$\int_a^bf\left(x\right)=f'\left(b\right)-f'\left(a\right)\$

c)

$\int_a^bF\left(x\right)=f\left(b\right)-f\left(a\right)\$ where F is the antiderivative

d)

$\int_a^bF\left(x\right)=f'\left(b\right)-f'\left(a\right)\$ where F is the antiderivative

75.

The fundamental theorem of calculus.

a)

$\frac{d}{dx}\int_0^xf\left(t\right)dt=f\left(x\right)$

b)

$\frac{d}{dx}\int_0^xf\left(t\right)dt=F\left(x\right)$ where F is the antiderivative

c)

$\frac{d}{dx}\int_0^xF\left(t\right)dt=f\left(x\right)$ where F is the antiderivative

d)

$\frac{d}{dx}\int_0^xf\left(t\right)dt=f'\left(x\right)$

76.

Volume using discs revolving around horizontal line.

a)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

b)

$\pi\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

c)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)^2dx\ \$

d)

$\int_{x=a}^{x=b}\left(top\ -bottom\right)dx\ \$

77.

Volume using discs revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

c)

$\int_{y=a}^{y=b}\left(right\ -left\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}\left(right\ -left\right)dy\ \$

78.

Volume using washers revolving around vertical line.

a)

$\pi\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

b)

$\pi\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

c)

$\int_{y=a}^{y=b}\left(R-r\right)^2dy\ \$

d)

$\int_{y=a}^{y=b}R^2-r^{2\ }dy\ \$

79.

If f'(x) = 0 what does that imply about the x value?

a)

It is a critical point, it is a possible max, min, or point of inflection.

b)

That the limit does not exist.

80.

When looking for critical points we did....

a)

took the limit of the function. 2. Graphed the critical points.

b)

Found f'(x). 2. Set f'(x) = 0 and solved for x. 3. Created a sign diagram. 4. Took the limit

c)

Found f'(x). 2. Set f'(x) = 0 and solved for x. 3. Created a sign diagram. 4. Checked out intervals.

81.

(a)

82.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

83.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

84.

Given the following integral values, find the integral below

a)

A

b)

B

c)

C

d)

D

85.

If $\int_0^2f\left(x\right)\ dx=5$ , $\int_2^4f\left(x\right)dx=3$ , and $\int_2^6\ f\left(x\right)dx\ =12$ , then $\int_0^6\ f\left(x\right)\ dx=$

a)

5

b)

-5

c)

17

d)

-17

86.

If a<c<b, answer the following:

a)

A

b)

B

c)

C

d)

D

e)

E

87.

$\int_{-3}^3\left|x+1\right|dx=$

a)

10

b)

0

c)

8

d)

none of these

88.

What is the derivative of y= 1 - x² + x - 3x⁴

a)

y^/=x+-2x+1-12x³

b)

y^/=x-x³/3+x²/2-3x⁵/5

c)

y^/=-2x+1-12x³

d)

y^/=2x+1-12x³

89.

what is the derivative of y= sin(2x)?

a)

y^/=cos(2x)

b)

y^/=2sin(2x)

c)

y^/=2sin(x)+cos(2x)

d)

y^/=2cos(2x)

90.

when is the function f(x)=x²+6x+9 increasing?

a)

(3,∞)

b)

(-∞,3)

c)

(-3,-∞)

d)

(-3,∞)

91.

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

92.

What is the integral of f(x)=sin(2x)+1/x

a)

-2cos(2x)+ln(x)+c

b)

ln(|x|)−cos(2x)/2+C

c)

ln(|x|)−cos(2x)/2

d)

ln(|x|)+cos(2x)/2+C

93.

Let f be the function defined by f(x)=4x³-10x+5. Find the equation of the tangent line to the graph of f at the point where x = 1

a)

y+1=2(x-1)

b)

y-1=2(x-1)

c)

y+1=2(x+1)

d)

y+1=-2(x-1)

94.

If g is the inverse function of F and f(2)=3, find the value of g'(3) for F(x)=6x²+2x-1

a)

1/24

b)

1/25

c)

1/26

d)

26

95.

What are the vertical asymptotes of the function f(x)=(x²-9)/(x²+6x+9)

a)

x=3

b)

x=-3

c)

x=3,-3

d)

no vertical asymptote

96.

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

a)

4

b)

2

c)

3

d)

23/4

97.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

98.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

99.

Alec consumes beverages at a rate of r(x)=10+.2x²beverages per hour, how many beverages does Alec drink in the first 16 hours?

a)

25.068

b)

433.067

c)

5463.759

d)

Too many, Alec should seek medical attention

100.

What is the derivative of the function f(x)=∫₁^2x(6e^x)dx

a)

6e^2x

b)

12e^2x

c)

6e^2x-6e^x

d)

6e^2x

101.

Find F'(x) given $F\left(x\right)=\int_0^{x^2}\csc^2x\ dx$

a)

$\csc^2\left(x^2\right)$

b)

$\csc^2\left(x\right)$

c)

$2x\csc^2\left(x\right)$

d)

$2x\csc^2\left(x^2\right)$

102.

$\int_{ }^{ }x\left(1-3x^2\right)^4dx$

a)

$\frac{-1}{30}\left(1-3x^2\right)^5$

b)

$\frac{-1}{30}\left(1-3x^2\right)^5+C$

c)

$\left(1-3x^2\right)^5+C$

d)

$\frac{-1}{6}\left(1-3x^2\right)^5+C$

103.

$\int_{ }^{ }\left[5^x-\csc^2x\right]dx$

a)

$5^x-\cot x+C$

b)

$5^x+\cot x+C$

c)

$\frac{5^x}{\ln5}+\cot x+C$

d)

$\frac{5^x}{\ln x}-\cot x+C$

104.

Approximate the area using a Midpoint Riemann Sum on the interval [0,4] for $f\left(x\right)=x^2+3$

a)

42

b)

26

c)

33

d)

66

105.

a)

A

b)

B

c)

C

d)

D

106.

a)

A

b)

B

c)

C

d)

D

107.

a)

A

b)

B

c)

C

d)

D

108.

a)

A

b)

B

c)

C

d)

D

109.

Hint: Use u substitution

a)

A

b)

B

c)

C

d)

D

110.

Integrate $\int\ \frac{1}{^3\sqrt{x}}\ dx$

a)

$\frac{2x^{\frac{3}{2}}}{3}+c$

b)

$\frac{3x^{\frac{2}{3}}}{2}+c$

c)

$\frac{3x^{\frac{2}{3}}}{2}$

d)

$6x^{\frac{3}{2}}+c$

111.

a)

A

b)

B

c)

C

d)

D

112.

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?

I. g has at least one horizontal tangent line.

II. g has at least 2 zeros.

III. For some c in the interval (3, 6), f'(c) = -7/3.

a)

II only

b)

II and III

c)

I and II

d)

I, II, and III

113.

s(t) = t² - 20
Find the average velocity from t = 3 to t = 5.

a)

2

b)

4

c)

6

d)

8

114.

An objects distance from its starting point at time t is given by the equation
s(t) = t³ - 6t² - 4.
What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

22

d)

44

115.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

a)

2

b)

4

c)

6.5

d)

7

116.

If $f'\left(a\right)=0$ and $f'\left(x\right)$ changes from positive to negative at $x=a$ , then $f\left(x\right)$ has

a)

A relative maximum at x=a

b)

A relative minimum at x=a

c)

No relative extrema at x=a

d)

A vertical tangent line at x=a

117.

Which of the following could be the graph of f ' , the derivative of f ?

a)

b)

c)

d)

e)

118.

On what interval(s) is the function $f\left(x\right)=x^3+6x^2$ concave down?

a)

$\left(-\infty,-4\right)$

b)

$\left(-\infty,-2\right)$

c)

$\left(-2,\infty\right)$

d)

$\left(0,\infty\right)$

119.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

120.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

121.

What is the limit of the function as x approaches 1 from the left?

a)

DNE

b)

1

c)

4

d)

-2

122.

What is the limit of the function as x approaches 1 from the right?

a)

DNE

b)

1

c)

4

d)

-2

123.

Selected values from the function f(x) are shown in the table. When a midpoint Riemann sum with two subintervals is used to complete $\int_2^{10}f\left(x\right)dx$ , the value is...

a)

24

b)

28

c)

36

d)

26

124.

$\frac{dy}{dx}=e^{x+3}y^3$

What would be a step in solving the differential equation?

a)

$\int y^3dy=\int e^{x+3}dx$

b)

$\int\ \frac{1}{y^3}dy=\int\ e^{x+3}dx$

c)

$\int\ \frac{1}{y^3}dy=\int\ \frac{1}{e^{x+3}}dx$

d)

$\int\ y^3dy=\int\ \frac{1}{e^{x+3}}dx$

125.

Let $g\left(x\right)=\ \int_0^xf\left(t\right)dt$ , where the graph of f is shown. For what value(s) of x does g have an inflection point?

a)

-2, 0, 5

b)

-2 and 5 only

c)

-2, 2, and 8

d)

2 and 8 only

126.

The graph of the function f is shown. At which of the following points is f'(x)<0 and f"(x)>0?

a)

c

b)

a

c)

b

d)

d

127.

Selected values from the function f(x) are shown in the table. When a left Riemann sum with two subintervals is used to approximate $\int_0^5f\left(x\right)dx$ , the value is...

a)

16

b)

21

c)

15

d)

11

128.

For a particle moving along the x-axis, x (1 )=5 and v (1)= 2. At time t = 1, it can be said that the particle is...

a)

Speeding up

b)

moving toward the origin

c)

moving away from the origin

d)

slowing down.

129.

$\frac{d}{dx}\left(e^{\frac{x}{5}}\right)=?$

a)

$-5e^{\frac{x}{5}}$

b)

$\frac{1}{5}e^{\frac{x}{5}}$

c)

$e^{\frac{x}{5}}$

d)

$5e^{\frac{x}{5}}$

130.

If $g\left(x\right)=\int_{\pi}^{\pi x}\cos\left(t^2\right)dt$ then $g'\left(x\right)=$

a)

$\sin\left(\pi^2x^2\right)$

b)

$\pi x\sin\left(\pi^2x^2\right)$

c)

$\pi x\cos\left(\pi^2x\right)$

d)

$\pi\cos\left(\pi^2x^2\right)$

131.

$\frac{\text{d}}{\text{d}x}\int_{\sin x}^4\sqrt{1+t^2}\ dt\ =$

a)

$\sqrt{1+\sin^2x}$

b)

$-\cos x\sqrt{1+\sin^2x}$

c)

$-\sqrt{1+\sin^2x}$

d)

$\cos x\sqrt{1+\sin^2x}$

132.

If f has two continuous derivatives on [5, 10] , then

\int_5^{10}f''\left(t\right)dt\ =\

a)

$f''\left(10\right)\ -\ f''\left(5\right)$

b)

$f'\left(10\right)\ -\ f'\left(5\right)$

c)

$f\left(10\right)\ -\ f\left(5\right)$

d)

$\frac{1}{5}\left(f'\left(10\right)\ -\ f'\left(5\right)\right)$

133.

The graph of $g'\left(x\right)$ is given below, if g(3) = 6 find g(0).

a)

1

b)

2

c)

4

d)

6

134.

The graph of f is given below. $F\left(x\right)=\int_0^x\ f\left(t\right)dt$ Which of the statements below is true?

a)

F is decreasing on (1,2)

b)

F has a relative minimum at x = 2

c)

F is decreasing on (2, 4)

d)

F has a relative maximum at x = 1.

e)

F has a point of inflection at x = 4.

135.

If

f\left(x\right)=\int_{-2}^xf'\left(t\right)dt\

where

f'\left(t\right)

is shown in the figure below, find the equation of the tangent line to f at

x=3

a)

y=18

b)

y = 2x + 18

c)

y = 2x + 12

d)

y = 2x + 2

136.

The function f(x) is continuous on the inteval [-5, 11], and selected values are given below. The trapezoidal approximation for $\int_{-5}^6f\left(x\right)dx$ found with 4 subintervals, is zero. Find k.

a)

-9/10

b)

-2/3

c)

-21/31

d)

-16/19

137.

$\int_0^{\pi}\cos x\ dx$

Which of the limits is equivalent to the following definite integral?

a)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{\pi i}{n}\right)\cdot\frac{\pi}{n}$

b)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{\pi i}{n}\right)\cdot\frac{i}{n}$

c)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{i}{n}\right)\cdot\frac{i}{n}$

d)

$\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{i}{n}\right)\cdot\frac{\pi}{n}$

138.

Given $g'\left(x\right)=\ln\left(x+7\right)$ and $g\left(2\right)\ =\ 6$ determine the value of $g\left(3\right)$ .

a)

-3.749

b)

1.648

c)

7.321

d)

8.250

139.

For a particle moving along the x-axis, $x\left(3\right)=-10$ and $v\left(3\right)=-9$ . At time t = 3, it can be said that the particle is ...

a)

Slowing down

b)

Moving away from the origin

c)

Moving toward the origin

d)

Speeding up

140.

Evaluate $\lim_{h\rightarrow0}\ \frac{\cos\left(\frac{7\pi}{6}+h\right)-\cos\left(\frac{7\pi}{6}\right)}{h}$

a)

$\frac{\sqrt{3}}{2}$

b)

$\frac{1}{2}$

c)

$-\frac{\sqrt{3}}{2}$

d)

$-\frac{1}{2}$

141.

If $g\left(x\right)=f^{-1}\left(x\right)$ , with $f\left(6\right)=2\ \&\ g\left(3\right)=2$ ,

then

g'\left(2\right)=?

a)

$f'\left(3\right)$

b)

$\frac{1}{f'\left(6\right)}$

c)

$\frac{1}{f'\left(3\right)}$

d)

$f'\left(6\right)$

142.

Let $g\left(x\right)=\int_0^x\ f\left(t\right)dt$ , where the graph of f is shown below. On what interval(s) is g both concave down and increasing?

a)

(-5, -2)

b)

(5, 8)

c)

cannot be determined

d)

(-5, -2) U (0, 2)

143.

If $g\left(x\right)=f^{-1}\left(x\right)$ , with $f\left(6\right)=5$ and $g\left(6\right)=8$ , then $g'\left(6\right)=?$

a)

$\frac{1}{f'\left(5\right)}$

b)

$\frac{1}{g'\left(8\right)}$

c)

$\frac{1}{f'\left(8\right)}$

d)

$\frac{1}{g'\left(5\right)}$

144.

Let $g\left(x\right)=\int_0^x\ f\left(t\right)dt$ , where the graph of f is shown. For what value(s) of x does g have a relative minimum?

a)

-2 and 2

b)

8

c)

-2 and 5

d)

2

145.

A particle's speed is decreasing if

a)

it's acceleration is positive

b)

it's velocity is positive

c)

it's velocity and acceleration have the same sign

d)

it's velocity and acceleration have different signs

146.

If Distance is a function of Time, what is the average rate of change from 6 to 9 seconds?

a)

3.3 feet per second

b)

-10 feet per second

c)

-3.3 feet per second

d)

10 feet per second

147.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

148.

a)

A

b)

B

c)

C

d)

D

149.

a)

A

b)

B

c)

C

d)

D

e)

E

150.

a)

A

b)

B

c)

C

d)

D

151.

a)

A

b)

B

c)

C

d)

D

152.

a)

A

b)

B

c)

C

d)

D

153.

a)

A

b)

B

c)

C

d)

D

154.

a)

A

b)

B

c)

C

d)

D

155.

a)

A

b)

B

c)

C

d)

D

156.

a)

A

b)

B

c)

C

d)

D

157.

a)

A

b)

B

c)

C

d)

D

158.

Which of these sums up the Mean Value Theorem (MVT)?

a)

$f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

b)

$f\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$f\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

d)

$f'\left(c\right)=\frac{f'\left(b\right)-f'\left(a\right)}{b-a}$

159.

Evaluate.

a)

-1

b)

3

c)

0

d)

The limit does not exist

160.

Evaluate.

a)

-3

b)

3

c)

-9

d)

The limit does not exist

161.

Evaluate.

a)

1/2

b)

2

c)

√2

d)

√2/2

162.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

C

c)

D

d)

E

e)

B

163.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

164.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

B

b)

C

c)

D

d)

E

165.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

C

c)

D

d)

E

166.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

E

167.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

D

d)

E

168.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

169.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

C

c)

D

d)

E

170.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

171.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

172.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

E

173.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

174.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

175.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

176.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

177.

Evaluate without a calculator. Show all steps on a sheet of paper.

a)

A

b)

B

c)

C

d)

D

178.

If

f'\left(x\right)=3e^{3x}\cos\left(e^{3x}\right)\

, then

f\left(x\right)=

?

a)

$\cos\left(e^{3x}\right)$

b)

$e^{3\sin\left(x\right)}$

c)

$\sin\left(e^{3x}\right)$

d)

$\sin\left(3e^{3x}\right)$

179.

Suppose that

$\lim_{\left(x\rightarrow-2^-\right)}f\left(x\right)=k$ , $\lim_{\left(x\rightarrow-2^+\right)}f\left(x\right)=k$ , and $f\left(-2\right)=k$ , then (Check all that apply)

a)

-2 is in the domain of $f\left(x\right)$

b)

$\lim_{\left(x\rightarrow-2\right)}f\left(x\right)$ exists

c)

$f\left(x\right)$ has a removal at x = -2

d)

$f\left(x\right)$ is continuous at x = - 2

e)

$f\left(x\right)$ must be differentiable at x = -2

180.

Suppose that $h\left(x\right)$ is continuous on the interval (2, 9) and that f(2) > 0 and f(9) < 0, then by the Intermediate Value Theorem

a)

$f\left(x\right)\$ is decreasing on the interval (2, 9)

b)

$f\left(x\right)\$ must have at least one x-intercept in the interval (2, 9)

c)

$f\left(x\right)$ has a positive Average Rate of Change on the interval (2, 9)

d)

$f\left(x\right)$ has at least one critical value in the interval (2, 9)

e)

$\lim_{\left(x\rightarrow2\right)}f\left(x\right)=9$

181.

Suppose that $f'\left(9\right)=0\ and\ f''\left(9\right)>0$ then $f\left(x\right)$ is (a) (two words) at x = 9.

182.

$\lim_{x\rightarrow\pi}\ \ \frac{\left(\cos\ x+\sin\left(2x\right)+1\right)}{x^2-\pi^2}\ =$ ___

a)

$\frac{1}{2\pi}$

b)

$\frac{1}{\pi}$

c)

1

d)

nonexistent

183.

If $f\left(x\right)=\left(x-1\right)\left(x^2+2\right)^3\ ,\ \ then\ f'\left(x\right)\ is$

a)

$6x\left(x^2+2\right)^2$

b)

$6x\left(x-1\right)\left(x^2+2\right)^2$

c)

$\left(x^2+2\right)^2\left(x^2+3x-1\right)$

d)

$-3\left(x-1\right)\left(x^2+2\right)^2$

e)

$\left(x^2+2\right)^2\left(7x^2-6x+2\right)$

184.

Evaluate $\lim_{h\rightarrow0}\ \frac{\tan^{-1}\left(x+h\right)-\tan^{-1}\left(x\right)}{h}$

a)

$\frac{1}{1+x^2}$

b)

$-\frac{1}{1+x^2}$

c)

$\frac{1}{\sqrt{1-x^2}}$

d)

$-\frac{1}{\sqrt{1-x^2}}$

185.

$\frac{d}{dx}\left(3^x\right)=?$

a)

$\frac{3^x}{\ln3}$

b)

$3^x\ln3$

c)

$3^x$

d)

$x3^{x-1}$

186.

$\int\sec x\tan xdx=?$

a)

$-\csc x+c$

b)

$-\sec x+c$

c)

$\csc x+c$

d)

$\sec x+c$

187.

When does a curve have a horizontal tangent line?

a)

When x = 0

b)

When y = 0

c)

When $\frac{\text{d}y}{\text{d}x}=0$

d)

When $\frac{\text{d}y}{\text{d}x}is\ undefined$

188.

When does a curve have a vertical tangent line

a)

When x = 0

b)

When y = 0

c)

When $\frac{\text{d}y}{\text{d}x}=0$

d)

When $\frac{\text{d}y}{\text{d}x}is\ undefined$

189.

If f''(x) < 0, the curve is

a)

Concave Up

b)

Concave Down

c)

Increasing

d)

Decreasing

190.

If f''(x) > 0, the curve is...

a)

Concave Up

b)

Concave Down

c)

Increasing

d)

Decreasing

191.

If f'(x) > 0, then f(x) is

a)

Concave Up

b)

Concave Down

c)

Increasing

d)

Decreasing

192.

If f'(x) < 0, then f(x) is

a)

Concave Up

b)

Concave Down

c)

Increasing

d)

Decreasing

193.

Which of the following uses the 1st Derivative Test correctly?

a)

f'(c)=0.

f'(x) changes from + to - at x=c.

Therefore, f(x) must have a relative minimum at x=c.

b)

f'(c)=0.

f'(x) changes from + to - at x=c.

Therefore, f(x) must have a relative maximum at x=c.

c)

f'(c)=0.

f''(c)<0.

Thus, f(x) has a relative maximum at x=c.

d)

f'(c)=0.

f''(c)>0.

Thus, f(x) has a relative minimum at x=c.

194.

Which of the following uses the 2nd Derivative Test for relative extrema correctly?

a)

f'(c)=0.

f''(c)>0.

Thus, f(x) must have a relative maximum at x=c.

b)

f'(c)=0.

f''(c)<0.

Thus, f(x) must have a relative minimum at x=c.

c)

f'(c)=0.

f''(c)>0.

Thus, f(x) must have a relative minimum at x=c.

d)

f''(c)=0.

f''(x) changes from + to - at x=c.

Thus, f(x) has a point of inflection at x=c.

195.

How can we tell if a function has a point of inflection at x=c?

a)

If f'(c)=0 and f'(x) changes signs at x=c

b)

If f'(c)=0

c)

If f''(c)=0 and f''(x) changes signs at x=c

d)

If f''(x)=0

196.

The graph shows the velocity of a body moving along a coordinate line in meters per second. When does the body reverse direction?

a)

t = 2, 6, 7

b)

t = 4, 8

c)

t = 3, -3

d)

t = 0, 9

197.

$\lim_{x\rightarrow2}\left(\frac{x-2}{x^2-7x+10}\right)$

(a)

198.

$\lim_{x\rightarrow0}\left(\frac{3x^2}{e^x-1-x}\right)$

(a)

199.

If the length L of a rectangle is decreasing at a rate of 2 inches per minute while its width W is increasing at a rate of 2 inches per minute, which of the following must be true about the area A of the rectangle?

a)

A is always increasing

b)

A is always decreasing

c)

A is increasing only when L>W

d)

A is increasing only when L<W

e)

A remains constant

200.

The side of a cube is increasing at a constant rate of 0.2 centimeters per second. In terms of the surface area S, what is the rate of change of the volume of the cube, in cubic centimeters per second?

a)

0.1S

b)

0.2S

c)

0.6S

d)

0.04S

e)

0.008S

201.

The function $f\left(x\right)=\left(1-\sin x\right)^2$ is concave up at $x=\frac{\pi}{6}$ ? What is the estimate for $f\left(0.5\right)$ using the local linear approximation for $f$ at $x\ =\ \frac{\pi}{6}$ ?

(a)

202.

The function $f\left(x\right)=\left(1-\sin x\right)^2$ is concave up at $x=\frac{\pi}{6}$ ? What is the estimate for $f\left(0.5\right)$ using the local linear approximation for $f$ at $x\ =\ \frac{\pi}{6}$ ? Is it an underestimate or overestimate?

a)

Underestimate

b)

Overestimate

203.

$\lim_{x\rightarrow0}\ \frac{1-\cos x}{1+x-e^x}=$

a)

-1

b)

0

c)

1

d)

nonexistent

204.

The graph of $f\ ',$ the derivative of f, is shown. For what values of x is the graph of f concave up?

a)

$b<x<d$

b)

$a<x<0$ or $x>d$

c)

$b<x<c$ or $x>e$

d)

$a<x<b$ or $c<x<e$

205.

Let $f\left(x\right)=\int_{-1}^{2x^4-x}e^tdt.$ At what value of x is f(x) a minimum?

a)

$0$

b)

$\frac{1}{2}$

c)

$\frac{1}{\sqrt[3]{2}}$

d)

$\frac{1}{\sqrt[]{2}}$

206.

Which of the following integrals gives the length of the graph of $y=1+4\ \sqrt[]{x^3}$ between x = 0 and x = 3?

a)

$\int_0^3\sqrt[]{1+36x}dx$

b)

$\int_0^3\sqrt[]{1+36x^2}dx$

c)

$\int_0^3\sqrt[]{1+36x^3}dx$

d)

$\int_0^3\sqrt[]{1+48x}dx$

207.

A population is modeled by a function P that satisfies the logistic differential equation $\frac{dp}{dt}=2P\left(1-\frac{P}{90}\right),$ where the initial population P(0) = 110 and t is the time in years. For what values of P is the population growing the fastest?

a)

30

b)

45

c)

55

d)

90

208.

Which of the following series can be used to determine if the series $\sum_{n=1}^{\infty}\frac{n^2+2n}{\sqrt[]{9+n^7}}$ converges, using the limit comparison test?

a)

$\sum_{n=1}^{\infty}\frac{1}{n^{\frac{1}{2}}}$

b)

$\sum_{n=1}^{\infty}\frac{1}{n^{\frac{3}{2}}}$

c)

$\sum_{n=1}^{\infty}\frac{1}{n^{\frac{5}{2}}}$

d)

$\sum_{n=1}^{\infty}\frac{1}{n^5}$

209.

Which of the following gives the area of the region inside the polar curve $r=2\sin\theta$ and outside the polar curve $r=\sin\theta?$

a)

$\frac{3}{2}\int_0^{\frac{\pi}{2}}\sin^2\theta d\theta$

b)

$2\int_0^{\frac{\pi}{2}}\sin^2\theta d\theta$

c)

$3\int_0^{\frac{\pi}{2}}\sin^2\theta d\theta$

d)

$4\int_0^{\frac{\pi}{2}}\sin^2\theta d\theta$

210.

Which of the following series converge?

I. $1+\frac{1}{2\sqrt[]{2}}+\frac{1}{3\sqrt[]{3}}+\frac{1}{4\sqrt[]{4}}+...$

II. $\frac{2}{5}-\frac{3}{6}+\frac{4}{7}-\frac{5}{8}+...$

III. $\sum_{n=1}^{\infty}\frac{n!}{1\cdot3\cdot5\cdot\cdot\cdot\left(2n+1\right)}$

a)

I only

b)

II only

c)

III only

d)

I and III only

211.

The fourth-degree Taylor polynomial for $xe^{-x}$ about x = 0 is

a)

$-1+x-x^2+\frac{x^3}{2}-\frac{x^4}{6}+...$

b)

$1-x+x^2-\frac{x^3}{2}+\frac{x^4}{6}-...$

c)

$-x+x^2-\frac{x^3}{2}+\frac{x^4}{6}-...$

d)

$x-x^2+\frac{x^3}{2}-\frac{x^4}{6}+...$

212.

If $\int_1^{\infty}\ \frac{\ln x}{x^2}dx=1,$ then which of the following must be true?

I. $\sum_{n=1}^{\infty}\frac{\ln n}{n^2}$ converges

II. $\sum_{n=1}^{\infty}\frac{\ln n}{n^2}$ diverges

III. $\sum_{n=1}^{\infty}\frac{\ln n}{n^2}=1$

a)

I only

b)

II only

c)

III only

d)

I and III only

213.

What are all values of x for which the series $\sum_{n=1}^{\infty}\left(-1\right)^n\frac{x^n}{n^23^n}$ converges?

a)

$-3<x<3$

b)

$-3\le x<3$

c)

$-3<x\le3$

d)

$-3\le x\le3$

214.

A function f has a Maclaurin series given by $1-\frac{x^4}{3!}+\frac{x^8}{5!}-\frac{x^{12}}{7!}+...+\frac{\left(-1\right)^{n-1}x^{4\left(n-1\right)}}{\left(2n-1\right)!}+...$ Which of the following is an expression for f(x)?

a)

$x\sin x$

b)

$x^2\cos x$

c)

$\frac{\sin\left(x^2\right)}{x^2}$

d)

$x^2e^{-x}-x^3$

215.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

216.

No Calc

a)

A

b)

B

c)

C

d)

E

217.

No Calc

a)

A

b)

B

c)

C

d)

D

218.

No Calc

a)

A

b)

B

c)

C

d)

D

219.

No Calc

a)

A

b)

B

c)

C

d)

D

220.

No Calc

a)

A

b)

C

c)

D

d)

E

221.

No Calc

a)

A

b)

B

c)

C

d)

D

222.

No Calc

a)

A

b)

C

c)

D

d)

E

223.

No Calc

a)

A

b)

B

c)

C

d)

D

224.

If $\lim_{x\rightarrow a}f\left(x\right)=f\left(a\right)$ which of the following must be true?

a)

f(x) is differentiable at x=a

b)

f(x) is continuous at x = a

c)

f(x) is differentiable and continuous at x=a

d)

none of these must be true

225.

If $\lim_{h\rightarrow0}\ \frac{f\left(2+h\right)-f\left(2\right)}{h}=5$ , which of the following must be true?

a)

The slope of the tangent line to f(x) at x=2 is 5

b)

The instantaneous rate of change of f(x) at x=2 is 5

c)

$f'\left(2\right)=5$

d)

all of these are true

226.

Evaluate the limit: $\lim_{h\rightarrow0}\ \frac{\cos\left(\pi+h\right)+1}{h}$

a)

$\pi$

b)

$-1$

c)

$1$

d)

$0$

227.

Determine the derivative: $\tan^2\left(2x\right)$

a)

$2\sec^2\left(2x\right)$

b)

$4\sec^2\left(2x\right)$

c)

$2\tan\left(2x\right)\sec^2\left(2x\right)$

d)

$4\tan\left(2x\right)\sec^2\left(2x\right)$

228.

What is the equation of the tangent line to $y=\frac{x+3}{x}$ when $x=1$

a)

$y-1=-3\left(x-1\right)$

b)

$y-4=-3\left(x-1\right)$

c)

$y-4=4\left(x-1\right)$

d)

$y-1=4\left(x-1\right)$

229.

If $h\left(x\right)=3\cdot f\left(x\right)-g\left(3x\right)$ , what is $h'\left(x\right)?$

a)

$3\cdot f'\left(x\right)-g'\left(3x\right)$

b)

$0\cdot f'\left(x\right)-g'\left(3\right)$

c)

$3\cdot f'\left(x\right)-3\cdot g'\left(3x\right)$

d)

$f'\left(x\right)-3\cdot g'\left(3x\right)$

230.

If it is known that $f\left(x\right)$ is a constant function and $h\left(x\right)=x\cdot f\left(x\right)$ , what is $h'\left(x\right)?$

a)

$0$

b)

$1\cdot f\left(x\right)$

c)

$1\cdot f'\left(x\right)$

d)

$x\cdot f'\left(x\right)$

231.

34.

a)

A

b)

B

c)

C

d)

D

e)

E

232.

a)

A

b)

B

c)

C

d)

D

e)

E

233.

a)

A

b)

B

c)

C

d)

D

e)

E

234.

a)

A

b)

B

c)

C

d)

D

e)

E

235.

a)

A

b)

B

c)

C

d)

D

e)

E

236.

76.

a)

A

b)

B

c)

C

d)

D

e)

E

237.

a)

a

b)

b

c)

c

d)

d

e)

e

238.

a)

a

b)

b

c)

c

d)

d

e)

e

239.

a)

a

b)

b

c)

c

d)

d

e)

e

240.

What is an antiderivative of $e^{3x}$ ?

a)

$e^{3x}$

b)

$3e^{3x}$

c)

$\frac{1}{3}e^{3x}$

d)

ln(3x)

241.

Which of these is an antiderivative of y = sec²x?

a)

tan x

b)

sec x

c)

cot x

d)

csc x

242.

a)

A

b)

B

c)

C

d)

D

e)

E

243.

a)

A

b)

B

c)

C

d)

D

e)

E

244.

a)

A

b)

B

c)

C

d)

D

e)

E

245.

Find g(2)

a)

-1/2

b)

-1

c)

1

d)

1/2

246.

Find g(-3)

a)

-2π

b)

-π

c)

π

d)

2π

247.

Find g'(2)

a)

-1/2

b)

-1

c)

1

d)

DNE

248.

Which choice below represents this slope field?

a)

dy/dx = 2x

b)

dy/dx = -x

c)

dy/dx = yx

d)

dy/dx = x²

249.

Find $f'\left(4\right)$

a)

-4

b)

$-\frac{1}{4}$

c)

$\frac{1}{4}$

d)

4

250.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

251.

Find $h'\left(-4\right)$

a)

-4

b)

-1/4

c)

1/4

d)

4

252.

Lef f be a function and let $f'\left(x\right)=x^2\left(x-2\right)\left(x+3\right)$ At how many points does the graph of f have a relative maxmimum OR minimum?

a)

0

b)

1

c)

2

d)

3

253.

a)

A

b)

B

c)

D

d)

E

254.

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

At what rate is the radius changing when the circumference is 100π ft?

a)

$\frac{dr}{dt}=\frac{20}{π}$

b)

$\frac{dr}{dt}=\frac{50}{π}$

c)

$\frac{dr}{dt}=50$

d)

$\frac{dr}{dt}=20$

255.

Where is the graph continuous yet NOT differentiable?

a)

x = a, b, c, d

b)

x = b, c, d

c)

x = a, b,

d)

x = b, d

256.

Given this graph of f'(x). On what interval(s) is f concave down?

a)

(-1,0) U (1,3)

b)

(-1,1) U (2,4)

c)

(0,1) U (3,4)

d)

(0,2)

257.

Find all relative extrema for the function above:

a)

A

b)

B

c)

C

d)

D

258.

Over what interval(s) is f(x) increasing?

a)

(-∞, -3) ∪ (1, ∞)

b)

(-3, 1)

c)

(-5, 0) ∪ (2, ∞)

d)

(-5, ∞)

259.

Identify the interval from the derivative graph where the function is concave down

a)

(-1,1) & (3,4)

b)

(-2,4)

c)

(-3,-1) & (1,3)

d)

(-2,1) & (1,4)

260.

$\left(1,\infty\right)$ Discuss the concavity and the point(s) of inflection (if any) of the function:

f\left(x\right)=x^3-3x^2+10

a)

Concave up in $\left(-\infty,1\right)$ , Concave down in $\left(1,\infty\right)$ . And the point of inflection at x = 1

b)

Concave down in $\left(-\infty,1\right)$ , Concave up in $\left(1,\infty\right)$ . And the point of inflection at x = 1

c)

Concave down in $\left(-\infty,\infty\right)$ . with no point of inflection.

d)

Concave up in $\left(-\infty,1\right)$ and $\left(1,\infty\right)$ . with no point of inflection.

261.

Discuss the concavity and the point(s) of inflection (if any) of the function:

f\left(x\right)=x^4-8x^3+x+2

a)

Concave up in $\left(-\infty,0\right)$ and , Concave down in (0, 4). And points of inflection at x = 0 and 4

b)

Concave down in $\left(-2,\ 2\right)$ and , Concave up in (0, 4). And points of inflection at x = 0 and 4

c)

Concave up in $\left(4,\infty\right)$ (0, 4) and ,With no points of inflection.

d)

Concave down in $\left(-\infty,-2\right)$ (0, 4) and ,With no points of inflection.

e)

Concave up in $\left(-\infty,\infty\right)$ ,With no points of inflection.

262.

Discuss the concavity and the point(s) of inflection (if any) for the function

f\left(x\right)=x^5-5x+2

a)

Concave down in $\left(-\infty,0\right)$ Concave up in ( $\left(0,\infty\right)$ ,. And Point of Inflection at x = 0

b)

Concave up in $\left(-\infty,0\right)$ Concave down in $\left(0,\infty\right)$ ,. And Point of Inflection at x = 0

c)

Concave down in $\left(-\infty,0\right)$ and $\left(0,\infty\right)$ . with no inflection point.

d)

Concave up in $\left(0,\infty\right)$ and $\left(0,\infty\right)$ . with no inflection point.

e)

Concave up in $\left(-\infty,\ \infty\right)$ with no inflection point.

263.

Given $f\left(x\right)=-6x^4-8x^3+2$

Use the 2nd Derivative Test to find and classify the relative extrema.

Select ALL that apply.

a)

Relative Maximum at

x = -1

b)

Relative Minimum at

x = 1

c)

Inflection at

x = 0

d)

Relative Maximum at

x = 1

e)

Relative Minimum at x = 0

264.

Given $f\left(x\right)=6x^5-10x^3+2$

Use the 2nd Derivative Test to find and classify the relative extrema.

Select ALL that apply.

a)

Relative Maximum at

x = -1

b)

Relative Maximum at

x = 1

c)

Inflection at

x = 0

d)

Relative Minimum at

x = 1

e)

Relative Minimum at x = 0

AP Calculus BC Review Sheet

Total questions: 264

Worksheet time: 9hrs 34mins

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