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Derivatives

Derivatives

Derivatives: Rolle With It True or False

1. f ' (x) = ->
2. Let f(x) = x2x. 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. 

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

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

 Insert Image DM-1

Which of the following could be the graph of f ' (x)? -> Image DM-4

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

Image DM-6

Which of the following could be the graph of f(x)? -> Image DM-10

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? ->  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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