Applications of Differentiation – Relative Extrema

Applications of Differentiation – Relative Extrema

Learning Objectives:

Understand and apply Applications of Relative Extrema

Applications of Differentiation – Relative Extrema

Definitions of Increasing Functions:

A function f is increasing on an interval for every a and b in the interval,

If b > a, then f (b) > f (a)

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 f (x) is increasing over the interval.

    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.

 

 

 

 

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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