Chapter Four Definitions and Theorems

# Chapter Four Definitions and Theorems - Chapter Four...

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Chapter Four: Applications of Differentiation Chapter Three showed us several techniques to differentiate a function. Chapter Four is going to show us several applications that involve the derivative. Definition: Extrema Let f be defined on an interval containing c. 1. ( ) f c is the minimum of f on I if ( ) ( ) f c f x for all x in I. 2. ( ) f c is the maximum of f on I if ( ) ( ) f c f x for all x in I. The minimum and maximum of a function f on an interval are called the extreme values, or extrema of the function on the interval. If I is equal to the domain of the function, then the minimum and maximum are called absolute. If a function has a “peak,” the y – value where the peak happens is called a relative maximum . If a function has a “valley,” the y – value where the valley happens is called the relative minimum. All absolute extrema on an open interval are relative extrema, but not all relative extrema are absolute extrema. Definition:

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## This note was uploaded on 06/21/2011 for the course MTH 150 taught by Professor Marioborha during the Summer '11 term at Moraine Valley Community College.

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Chapter Four Definitions and Theorems - Chapter Four...

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