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BC Fall Review

Total questions: 35

Worksheet time: 1hrs 26mins

Name
Class
Date
1.

Which one of the following statements is always true?

a)

When a graph is increasing, its derivative is negative.

b)

When a graph is decreasing, so is its derivative.

c)

When a graph is decreasing, its derivative is negative.

d)

When a graph is increasing, so is its derivative.

2.
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
3.
f''(x) is pictured. Which x values are inflection points of f(x)?
a)
x=-5 and -1
b)
x=-3
c)
x=4
d)
no inflection points
4.
a)

A

b)

B

c)

C

d)

D

5.
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
6.

Select the correct derivative of f(x).

a)

A.

b)

B.

c)

C.

d)

D.

7.
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
8.
f(x) is pictured. Inflection points are most likely at which x values?
a)
x=0 and 1.5
b)
x=2 and 2.5
c)
x=2.25
d)
x=1
9.
a)
Mean value theorem
b)
Rolle's theorem
c)
Intermediate Value Theorem
d)
Fundamental Theorem of Calculus
10.
When f'(x) changes from positive to negative, there is(are) ...
a)
a maximum.
b)
a minimum.
c)
no extrema.
11.

Which value is guaranteed by the MVT for the function given: f(x) = x2 - 6x + 8 on [0,3]

a)

f(c) = 10

b)

f(c) = 4

c)

f ' (c) = -3

d)

f ' (c) = 7/3

12.
If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?
a)
It's constant
b)
It's increasing
c)
It's decreasing
d)
Cannot be determined
13.

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed?

a)

g(0) = 0

b)

g'(c)= 0 for some c in (-1,3)

c)

g'(c)= 4 for some c in (-1, 3)

d)

g(c)= 4 for some c in (-1, 3)

14.
Given u = fg, f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,
then u'(2) = ?
a)
-12
b)
4
c)
5
d)
12
15.
Given v = f/g, f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,
then v'(2) = ?
a)
5
b)
-2
c)
nine fifths
d)
negative four thirds
16.
Given y = -3sinx, y' =
a)
⅓cosx
b)
3cosx
c)
-3cosx
d)
-⅓cosx
17.
Given y = x2 − sin x , y ' (π) = 
a)
π2 + 1 
b)
2π − 1
c)
2π + 1
d)
π2
18.
The derivative of 
a)
y'=2x-x-2
b)
y'=x-1+8x
c)
y'=x-2+8x
d)
y=8x-x-2
19.
a)
2 only
b)
0 only
c)
1 only
d)
0 and 2 only
20.
What is the limit of the function as x approaches 1 from the right?
a)
DNE
b)
1
c)
4
d)
-2
21.
What is the integral of k dx if k is a constant?
a)
k²/2  + C
b)
kx + C
c)
kx
d)
k²/2
22.
What is the integral of 1/u du?
a)
1/u2 + C
b)
lnu + c
c)
ln|u| + C
d)
1/u2 + C
23.
Use LRAM and 4 subintervals to estimate the area under the curve. You may use a calculator.
a)
A
b)
B
c)
C
d)
D
24.
f'(x)=6x5+7
f(-2)=30
Find C
a)
-20
b)
108
c)
50
d)
-34
25.
Find the derivative:
y = 4ex²
a)
y'=8xe
b)
y'=8xex²
c)
y'=8xe2x
d)
y'=8xe4x²
26.
Find this limit
a)
-2x+1
b)
-x2+x
c)
undefined
d)
2x-1
27.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

28.
a)

3/4

b)

3/10

c)

3/5

d)

25/10

29.

Based on the table, use a left Riemann sum with sub-intervals given by the table to estimate the area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

30.
a)
A
b)
B
c)
C
d)
D
31.

∫ sin (2x) dx

a)

cos(2x)+C

b)

-(1/2)cos(2x)+C

c)

-cos(2x)+C

d)

(1/2)cos(2x)+C

32.

∫ (2 - x)5 dx

a)

-5 (2 - x )4 + C

b)

( 2 - x )6 + C

c)

(1/6) ( 2 - x )6 + C

d)

-(1/6) ( 2 - x )6 + C

33.
a)
ln(2x2+6) + C
b)
ln(2x2+6)(4x) + C
c)
1/(2x2+6) + C
d)
1/(2x2+6)2 + C
34.

Rewrite the function in terms of u.

a)
b)
c)
d)
35.

Rewrite the function in terms of u.

a)
b)
c)
d)

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