3.1 Maximum and Minimum Values

# 3.1 Maximum and Minimum Values - Theorem 3.2 Relative...

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Maximum and Minimum Values Section 3.1

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Defn: Absolute Extreme Values Let f be a function with domain D. Then f(c) is the (1) absolute minimum of f on D iff f(c) < f(x) for all x in D. (2) absolute maximum of f on D iff f(c) > f(x) for all x in D.
The Extreme Value Thm. If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.

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Defn: Local Exteme Values l Let c be an interior point of the domain of the function f . Then f(c) is a l local maximum value at c iff f(c) > f(x) when x is near c. l local minimum value at c iff f(c) < f(x) when x is near c.
Fermat’s Theorem

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Relative extrema & critical #s

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Unformatted text preview: Theorem 3.2 Relative minimums/maximums occur only at critical numbers. Critical Numbers Finding Extrema On a Closed Interval (1) Find the critical #s of f in (a , b). (2) Evaluate f at each critical # in (a , b). (3) Evaluate f at each endpoint of [a , b]. (4) The least of these values is the minimum. The greatest is the maximum. Joke Time What kind of undergarment does Little Mermaid wear? an Alge-bra Why did the man sleep with a ruler? to see how long he could sleep l What did the little acorn say when he grew up? l Ge-om-o-try...
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## This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

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3.1 Maximum and Minimum Values - Theorem 3.2 Relative...

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