Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ'

Practice Questions

AP Calculus AB › Relationship between the increasing and decreasing behavior of ƒ and the sign of ƒ'

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1

Find the derivative of g(t) and tell whether g(t) is increasing or decreasing on the interval \[5,6\].

2

Determine the intervals on which the function is decreasing:

$f=\frac{x^5}{5}+x^3-4x$

3

Determine the relative maxima of the following function:

$f=\frac{x^5}{5}-\frac{13x^3}{3}+36x$

4

Find the intervals on which the function is decreasing:

$f=\frac{x^4}{4}-{\frac{x^3}{3}}-2x^2+4x$

5

Determine the intervals on which the function is decreasing:

6

Determine the intervals on which the function is increasing:

$f=\frac{x^5}{5}-\frac{26}{3}x^3+25x$

7

Find the intervals on which the function is decreasing:

$f=\frac{x^4}{4}+x^3-2x^2-12x$

8

Find the intervals on which the function is decreasing:

$g=\frac{x^2}{2}-5x$

9

Determine the intervals on which the following function is increasing:

$f=\frac{x^3}{3}-x$

10

Determine the intervals on which the function is increasing:

$f(x)=\frac{x^3}{3}+2x^2-10x$

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