1.
f' (x ) = -> $$\lim_{h\to0}\frac{f (x + h)-f (x)}{h}$$
True
False

2.
Let f (x ) = x ^{2} - x . Calculate f' (x ).

-> f' (x ) = -2x - 1
True
False

3.
If f' (x ) = 4x ^{2} + 3, find f' (-2 ).

-> There is insufficient information to answer this question.
True
False

4.
If f (x ) is a line of the form f (x ) = mx + b then

-> f' (x ) = m
True
False

5.
A graph of the function f ( x ) is shown below.

PICTURE mult choice 3-3

The function f' (x ) is -> always negative
True
False

6.
A graph of the function f ( x ) is shown below.

PICTURE mult choice 3-1 without red

Which of the following could be the graph of f' (x )? -> PICTURE: mult choice 3-1c
True
False

7.
A graph of f' (x ) is shown below.

PICTURE mult choice 3-2 without red

Which of the following could be the graph of f (x )? -> PICTURE: mult choice 3-2d
True
False

8.
If

f is differentiable on (a , b ), and f ( a ) = f ( b ), then Rolle's Theorem tells us -> the number of values c in (a , b ) for which f '(c ) = 0.

True
False

9.
For which given function and interval are we allowed to use the Mean Value Theorem? -> f (x ) = \frac{1}{x^{2} } on (0,2)
True
False

10.
What does the Mean Value Theorem tell us about the function f (x ) = x ^{3} on the interval (-2,1)?

-> There is some c in (-2,1) with f '(c ) = 3.

True
False