3.1: Increasing and Decreasing Functions

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Presentation transcript:

3.1: Increasing and Decreasing Functions

Definition 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)

Look at y = x2. What do you notice about the slopes?

Increasing/Decreasing Test 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).

Use the I/D Test for y = x2. What is the derivative? Where is the derivative positive? Where is the derivative negative?

Checkpoint 2 p. 185

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

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Example Find the intervals on which is increasing and decreasing.

Now you try: Determine the intervals on which the following functions are increasing/decreasing.

Last Example Checkpoint 6 p. 190