
Mean Value and Rolle's Theorem
Authored by Lisa Lee
Mathematics
11th Grade - University

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20 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Let f be the function defined by f(x) = x3+x-4. What is the value of c for which the instantaneous rate of change of f at x=c is the same as the average rate of change of f over [-1, 3].
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If f(x)=x3, at what point on the interval 0<x<3 is the tangent to the curve parallel to the secant line for this interval?
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If f(x)=sin(x/2), at what point on the interval π/2<x<3π/2 is the tangent to the curve parallel to the secant line for this interval?
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
On the closed interval [-2,3], the absolute maximum value(s) of f(x) = x3-3x2+12 occurs at x =
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Suppose that f is differentiable for all reals. For x in the interval (-5, 0), suppose that f'(x)<0. For x in the interval (0, 5), suppose that f'(x) >0. Then at x = 0 it must be true that f has
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Suppose that f is differentiable for all reals. For x in the interval (-∞, 4), suppose that f'(x)>0. For x in the interval (4, ∞), suppose that f'(x) <0. Then at x = 4 it must be true that f has
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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?
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