Learning Objectives:

__Applications of Differentiation – Relative Extrema__

*Definitions of Increasing Functions:*

A function ** f** is increasing on an interval for every

If ** b > a**, then

*Procedure to determine where a function is increasing or decreasing and Relative Extrema:*

1. Locate the critical values or numbers of ** f**. Use these numbers to determine test intervals. Also include points of discontinuity.

2. Determine the sign of ** f’(x)** in each interval.

3. If ** f’(x) > 0**, then

If ** f’(x) < 0, then f (x)** is decreasing over the interval.

4. Based upon the sign changes of ** f’(x)** determine if a relative maximum, relative minimum, or neither exist.

5. If relative extrema exist find them by evaluating the original function at the x- value.

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**Hook questions:**

*1. What is Increasing Function? *

*2. State the procedure to determine a function is increasing or decreasing and Relative Extrema.*

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