A function f is increasing on an interval if for any 2 numbers x1 and x2 in the interval

x1<x2 implies f(x1) < f(x2)

A function f is decreasing on an interval if for any 2 numbers x1 and x2 in the interval x1<x2 implies f(x1) > f(x2)

If f’(x) > 0 for all x in the interval (a, b), then f is increasing on the interval (a, b).

If f’(x) < 0 for all x in the interval (a, b), then f is decreasing on the interval (a, b).

If f’(x) = 0 for all x in the interval (a, b), then f is constant on the interval (a, b).

What is the derivative?

Where is the derivative positive?

Where is the derivative negative?

If f is defined at c, then c is a critical number of f if f’(c) = 0 or f’(c) is undefined.

Find f’(x) Locate critical numbers Set up a number line, test x-values in each

interval

Find the intervals on which f(x) =x3 – 12x is increasing and decreasing.

Find the intervals on which is increasing and decreasing.

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f x( ) = x2

3

Determine the intervals on which the following functions are increasing/decreasing.

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f x( ) =x 3

4− 3x

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f x( ) =x 2

x +1

Checkpoint 6 p. 190