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Absolute Extrema

Learn how to find the absolute extrema of a function over a closed interval using critical points and endpoints. Understand the difference between absolute, relative, maximum, and minimum values.

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Absolute Extrema

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  1. Absolute Extrema

  2. Objective • To find the absolute extrema of a continuous function on a closed interval.

  3. Absolute Extrema • The terms relative minimum and relative maximum describe the local behavior of a function. • To describe the global behavior of the function on an entire interval, you can use the terms absolute maximum and absolute minimum.

  4. Absolute Extrema y Absolute maximum Relative maximum Relative minimum Absolute minimum x b a

  5. Absolute Extrema • To find the absolute extrema of a continuous function f on a closed interval [a, b] , use the following steps: • Evaluate f at each of its critical points in (a, b) . • Evaluate fat each endpoint. • The least of these values is the absolute minimum, and the greatest is the absolute maximum.

  6. Absolute Extrema • Find the absolute extrema of :

  7. Absolute Extrema • Find the absolute extrema of : Abs. min Abs. max

  8. Absolute Extrema Abs. max Abs. min

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