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Quizzes

1. f'(x) = -> $$\lim_{h\to0}\frac{f(x + h)-f(x)}{h}$$
2. Let f(x) = x2 - x. Calculate f'(x).

-> f'(x) = -2x - 1

3. If f'(x) = 4x2 + 3, find f'(-2).

-> There is insufficient information to answer this question.

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

-> f'(x) = m

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

 PICTURE mult choice 3-3

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

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

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

8. If 

  •  f is continuous on [a,b
  • 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.


9. For which given function and interval are we allowed to use the Mean Value Theorem? -> f(x) = \frac{1}{x2} on (0,2)
10. What does the Mean Value Theorem tell us about the function f(x) = x3 on the interval (-2,1)?

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


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