R3ps - Chapter 3 Application of derivatives(Review Stephen...

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Chapter 3 Application of derivatives. (Review) Stephen Suen Chapter 3 Application of derivatives – p. 1/16
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3.1 Increasing/decreasing prop- erties of functions Suppose that f is differentiable on ( a, b ) . f is ր on ( a, b ) iff f ( x ) > 0 for x in ( a, b ) . f is ց on ( a, b ) iff f ( x ) < 0 for x in ( a, b ) . The places ( x -values) at which f can change from ր to ց , or from ց to ր , are f ( x ) = 0 , or f ( x ) is undefined . These are candidates where the monotonicity of f can change. Chapter 3 Application of derivatives – p. 2/16
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3.1.1 Steps for finding intervals on which f is ր or ց Find f (if not given). Determine values of x at which (a) f ( x ) = 0 , (b) f ( x ) is undefined. Use these values of x to divide the real line into intervals Table, with rows: intervals , test values , sign of f ( x ) , conclusion . Chapter 3 Application of derivatives – p. 3/16
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3.2 Extrema There are two main types of extrema: relative and absolute . Also, each extremum can be a maximum or a minimum . Note that for a function on a closed interval, absolute extrema can occur at the endpoint(s) of the interval. Chapter 3 Application of derivatives – p. 4/16
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a function f 1 . Follow the steps for finding the monotone properties of f . 2 . Determine the critical numbers : These are values of x where x is in the domain of f , (i.e. f ( x ) is defined,) and either (a) f ( x ) = 0 , or (b) f ( x ) is undefined. 3
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.

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R3ps - Chapter 3 Application of derivatives(Review Stephen...

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