Use Mean Value Theorem, Extreme Value Theorem, and Critical Points

Practice Questions

Calculus AB › Use Mean Value Theorem, Extreme Value Theorem, and Critical Points

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1

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

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

2

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

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

3

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

4

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

5

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

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

6

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

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

7

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?

8

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?

9

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

10

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

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