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Derivatives: Rolle With It Quiz

Think you’ve got your head wrapped around Derivatives? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. f ' (x) =


Q. Let f(x) = x2x. Calculate f ' (x).



f ' (x) = 2x + 1

f ' (x) = 2x – 1
f ' (x) = -2x – 1
f ' (x) = -2x + 1
Q. If f ' (x) = 4x2 + 3, find f ' (-2).



11
-19
19
There is insufficient information to answer this question.
Q. If f(x) is a line of the form f(x) = mx + b then



f ' (x) = m
f ' (x) = mx
f ' (x) = b
f ' (x) = 0
Q. A graph of the function f(x) is shown below. 

 The function f ' (x) is



always positive
always negative
positive when x is less than zero and negative when x is greater than zero.
negative when x is less than zero and positive when x is greater than zero.
Q. 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-2
Image DM-3
Image DM-4
Image DM-5
Q. A graph of f ' (x) is shown below.

Image DM-6

Which of the following could be the graph of f(x)?



Image DM-7
Image DM-8
Image DM-9
Image DM-10
Q. 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.

that there is some c in (a, b) with f ' (c) = 0.

that there are infinitely many values of c in (a, b) with f ' (c) = 0.

the precise value(s) of c in (a, b) for which f ' (c) = 0.

Q. For which given function and interval are we allowed to use the Mean Value Theorem?


f(x) = |x| on (-1,1)

 on (0,2)
f(x) = x2x on (-2, -1)

 on (-1, 1)
Q. What does the Mean Value Theorem tell us about the function f(x) = x3 on the interval (-2,1)?



Nothing. We aren't allowed to use the Mean Value Theorem here.
There is some c in (-2,1) with f ' (c) = 0.

f ' (0) = 3.

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