R3 - Chapter 3 Application of derivatives. (Review) Stephen...

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Unformatted text preview: Chapter 3 Application of derivatives. (Review) Stephen Suen Chapter 3 Application of derivatives – p. 1/16 3.1 Increasing/decreasing prop- erties of functions Suppose that f is differentiable on ( a, b ) . Chapter 3 Application of derivatives – p. 2/16 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 ) > for x in ( a, b ) . Chapter 3 Application of derivatives – p. 2/16 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 ) > for x in ( a, b ) . • f is ց on ( a, b ) iff f ′ ( x ) < for x in ( a, b ) . Chapter 3 Application of derivatives – p. 2/16 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 ) > for x in ( a, b ) . • f is ց on ( a, b ) iff f ′ ( x ) < for x in ( a, b ) . • The places ( x-values) at which f can change from ր to ց , or from ց to ր , are Chapter 3 Application of derivatives – p. 2/16 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 ) > for x in ( a, b ) . • f is ց on ( a, b ) iff f ′ ( x ) < 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 . Chapter 3 Application of derivatives – p. 2/16 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 ) > for x in ( a, b ) . • f is ց on ( a, b ) iff f ′ ( x ) < 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 3.1.1 Steps for finding intervals on which f is ր or ց • Find f ′ (if not given). Chapter 3 Application of derivatives – p. 3/16 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 Chapter 3 Application of derivatives – p. 3/16 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 , Chapter 3 Application of derivatives – p. 3/16 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. Chapter 3 Application of derivatives – p. 3/16 3.1.1 Steps for finding intervals on which f is ր or ց • Find f ′ (if not given)....
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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 - Tampa.

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R3 - Chapter 3 Application of derivatives. (Review) Stephen...

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