This preview shows pages 1–13. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ( xvalues) 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 ( xvalues) 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 ( xvalues) 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)....
View
Full
Document
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.
 Fall '08
 DANIELYAN
 Calculus, Derivative

Click to edit the document details