Free Printable Calculus Pt. I Praxis Prep

1.

Using this graph of f’(x), find the slope of the line tangent to f(x) at point c

a)

0

b)

1

c)

-1

d)

Not enough information

2.

Find the slope at x = 3 of the equation f(x) = 3x²

a)

6x

b)

27

c)

18

d)

3x

3.

Differentiate y= x³ + 2x

a)

3x³+2x

b)

3x²+2

c)

3x+2

d)

3x

4.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

5.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

6.

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.

7.

$\lim_{x\rightarrow1}\left(\frac{\ln x}{x-1}\right)$

a)

1

b)

0

c)

$\frac{1}{2}$

8.

a)

-1

b)

1

c)

0

d)

12

9.

Find the average rate of change on the interval $\left[a,a+h\right]$

a)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{a}\right)$

b)

$\left(\frac{f\left(a+h\right)-f\left(a\right)}{h}\right)$

c)

$\left(\frac{f\left(a\right)-f\left(a+h\right)}{h}\right)$

d)

$\frac{f\left(a+h\right)}{f\left(a\right)}$

10.

If the position of a particle is represented by s(t) = t² + 2, what is its instantaneous velocity at t = 3?

a)

5 ft/sec

b)

6 ft/sec

c)

3 ft/sec

d)

4 ft/sec

11.

Determine the interval over which the function is decreasing.

a)

(- $∞$ , -1.549) U (0.215, $∞$ )

b)

(-1.549, 0.215)

c)

(- $∞$ , 0.631) U (-2.133, $∞$ )

d)

(-2.133, 0.631)

12.

Describe the curvature of

f(x) = 2x² - 7x + 3

a)

Concave down

b)

Concave up

c)

Concave down then concave up

d)

Concave up then concave down

13.

Which function has no concavity?

a)

Linear

b)

Quadratic

c)

Cubic

d)

All functions have concavity

14.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

15.

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

16.

As x gets close to 1, then $\frac{x^2-1}{x-1}$ gets close to

a)

1.5

b)

1.9

c)

1.99

d)

2

17.

If the limit of a rational function produces 0/0 form, the following should be done EXCEPT

a)

Derive each term in the function

b)

Divide out the common factor(s)

c)

Re-evaluate the limit

d)

Add its variables

18.

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

a)

b)

c)

d)

e)

19.

Identify the critical points of the following function:
g(x)=2x³-3x²

a)

x=-1,1

b)

x=0,0

c)

x=0,-1

d)

x=0,1

20.

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

21.

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

a)

increasing

b)

decreasing

c)

concave up

d)

concave down

22.

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

23.

The function $f\left(x\right)=-x^3+3x^2-5$ has a relative maximum value of _____________ at x=_____________.

a)

0; -5

b)

-5; 0

c)

2; -1

d)

-1; 2

24.

The concavity of a function is described by its _______________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

25.

What will be true at an inflection point? (select the best answer)

a)

f(x)=0

b)

f'(x)=0

c)

f''(x)=0

d)

The function is undefined

26.

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)

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

27.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

28.

a)

Does not exist

b)

2

c)

0

d)

1

29.

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

a)

2

b)

-4

c)

DNE

d)

-2

30.

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

a)

y = 500x + 400

b)

y = 100x + 400

c)

y = -500 x - 400

d)

y = 500x - 400

31.

Set up the derivative of y=(3x⁴- 7)*(5x²+ 1)

a)

(12x³)*(10x)

b)

(3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

c)

(3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

d)

(3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

32.

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

33.

What is f'(x) if f(x) = cos(5x⁴)?

a)

f'(x) = sin(20x³)

b)

f'(x) = 20x³ sin(5x⁴)

c)

f'(x) = -sin(20x³)

d)

f'(x) = -20x³ sin(5x⁴)

34.

a)

1/2

b)

-1/2

c)

0

d)

3/2

35.

find y' for y=(e^5x)+1

a)

5e^5x+1

b)

e^5x

c)

5e^5x

d)

1

36.

The second derivative of a function is given by $f''\left(x\right)=0.5+\cos\left(x\right)-e^{-x}$ . Over the interval $\left[-2,4\right]$ the graph of the function $f$ changes from concave up to concave down at approximately $x=$

a)

-0.36

b)

0.59

c)

1.93

d)

3.10

37.

Let $f\left(x\right)=x^3-7x^2+25x-39$ and let $g$ be the inverse function of $f$ . What is the value of $g'\left(0\right)$ ?

a)

25

b)

10

c)

$\frac{1}{25}$

d)

$\frac{1}{10}$

38.

L(t) represents the total number of lollipops that a class has eaten after t minutes. What does L'(10) = 12 represent?

a)

At t = 10 minutes, the class is eating lollipops at a rate of 12 lollipops per minute.

b)

At t = 10 minutes, the class has eaten 12 lollipops.

c)

At t = 10 minutes the rate at which the class is eating lollipops is increasing at a rate of 12 lollipops per minute per minute.

d)

At t = 12 minutes the class has eaten 10 lollipops.

39.

a)

A

b)

B

c)

C

d)

D

e)

E

40.

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.

Calculus Pt. I Praxis Prep

Total questions: 40

Worksheet time: 1hrs 20mins

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