Extreme Values of Functions

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Presentation transcript:

Extreme Values of Functions 4.1 Extreme Values of Functions

Quick Review

Quick Review

Quick Review Solutions

Quick Review Solutions

What you’ll learn about Absolute (Global) Extreme Values Local (Relative) Extreme Values Finding Extreme Values Essential Questions How do we find the maximum and minimum values of a function, called optimization? How do we use this in real-world problems?

Absolute Extreme Values 1. Find the absolute extrema for the following functions on the given domain. Function Rule Domain D Absolute Extrema on D No absolute maximum. Absolute minimum of 0 at x = 0. Absolute maximum of 4 at x = 2. Absolute minimum of 0 at x = 0. Absolute maximum of 4 at x = 2. No absolute minimum. No absolute extrema.

The Extreme Value Theorem

Classifying Extreme Values

Local Extreme Values

Local Extreme Values Critical Points 2. Find the absolute maximum and minimum values of on the interval [-2, 3]. Critical value at x = 0. Absolute Maximum is 2.08 at x = 3. Absolute Minimum is 0 at x = 0.

3. Since the graph has no endpoints, all the extreme values must occur at critical points. Domain: (-3, 3) The only critical value is at x = 0. Absolute Minimum is 1/3 at x = 0. No Maxima, either local or absolute.

Pg. 193, 4.1 #1-41 odd