L19 - Lecture 19 Relative Extrema Example: A rational...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 19 — Relative Extrema Example: A rational function and increasing, de- creasing intervals Find all critical points for the function f ( x ) = 4 x + 1 x . Find the intervals on which f is increasing and de- creasing.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sketch the graph of f ( x ) = 4 x + 1 x
Background image of page 2
Relative Extrema and the First Derivative Test Definition: Let y = f ( x ) and let c be in the domain of f . Then 1) f ( c ) is a relative maximum of f if there is an open interval ( a,b ) containing c so that for all x in the interval ( ) . 2) f ( c ) is a relative minimum of f if there is an open interval ( ) containing c so that for all x in the interval ( ) . NOTE:
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Where do relative extrema occur for a continuous function? Examples: We note the following: If f has a relative extreme value at x = c , then That is, c is a critical point of f .
Background image of page 4
The First Derivative Test for Finding Relative Ex- trema Suppose that f is continuous on an interval contain- ing a single critical point x = c . If f is differentiable on the interval (except possibly at c ), then 1) f ( c ) is a relative maximum if f 0 ( x ) changes sign
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/27/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

Page1 / 11

L19 - Lecture 19 Relative Extrema Example: A rational...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online