# chapter4 - MATH1010 Chapter 4 cont 1 APPLICATIONS OF...

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MATH1010: Chapter 4 cont… 1 APPLICATIONS OF DERIVATIVES cont … Maximum and Minimum Values (Section 4.1, pg. 279) cont… Recall: Last day, we looked at max and min values, but we explored this concept graphically. Example: Sketch a graph of a continuous function f such that the absolute maximum of ) ( x f on the interval (-1, 1) does not exist and the absolute minimum equals 3. Recall: Last day, we discussed the Extreme Value Theorem which states that on a closed interval, a continuous function attains both an absolute max and an absolute min. Fermat’s Theorem: If f has a local maximum or minimum at c, and if ) ( c f exists, then 0 ) ( = c f . Caution: Some Important Points Are all places where the derivative is zero a local max/min?

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MATH1010: Chapter 4 cont… 2 Do local max/min occur only at places where the derivative is zero? Definition: A critical number of a function f is a number c in the domain of f such that either 0 ) ( = c f or ) ( c f does not exist. So, rephrasing
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## This note was uploaded on 09/13/2008 for the course MATH 1010u taught by Professor Kim during the Spring '08 term at Trinity University.

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chapter4 - MATH1010 Chapter 4 cont 1 APPLICATIONS OF...

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