Mean Value Theorem

Practice Questions

AP Calculus AB › Mean Value Theorem

Questions

9

1

Find the area of the region enclosed by the parabola $y=12-x^2$ and $y=-x$ .

2

Consider the region bounded by the functions

$f(x) = -x^{2} + 2x$ and

$g(x) = -sin(\frac{\pi x}{2})$

between and . What is the area of this region?

3

Find the mean value of the function over the interval $(0,\frac{\pi}{2})$ .

4

is continuous and differentiable on $\mathbb{R}$ .

The values of for five different values of are as follows:

Which of the following is a consequence of Rolle's Theorem?

5

Find the area under the curve $f(x)=\frac{1}{\sqrt{x+2}}$ between $2\leq x\leq 7$ .

6

Let $f(x) = x^{4}+ 6x - 17$ .

True or false: As a consequence of Rolle's Theorem, has a zero on the interval .

7

$f(x) = x^{3} - 7x + 16$

As a consequence of the Mean Value Theorem, there must be a value $c \in (-2, 2 )$ such that:

8

Find the area bounded by $y=2, y=x, y=\frac{1}{9}x^2, x=3$

9

$\int _0^\pi sin(x) dx$

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