lecture23

lecture23 - a,b 3 Find the absolute extrema of f on a,b...

This preview shows pages 1–12. Sign up to view the full content.

Lecture 23 1 Lecture 23, (Sec. 4.4) Absolute Extrema ex. Find all relative extrema of f ( x ) = x 2 - x 4 2 .

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

View Full Document
Lecture 23 2 Sketch the graph of f ( x ) = x 2 - x 4 2 .
Lecture 23 3 Given a function f and an x -value c in the domain of f . The function value f ( c ) is the absolute maximum value of f if for each x in the domain of f , The function value f ( c ) is the absolute minimum value of f if for each x in the domain of f ,

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

View Full Document
Lecture 23 4 Absolute Extrema on an Interval: How to ﬁnd it? If f is continuous on an open interval I and c is the only critical value on the interval: 1) 2)
Lecture 23 5 ex. Find the absolute extrema of f ( x ) = x 2 + 18 x - 3 on (0 , ).

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

View Full Document
Lecture 23 6 Absolute Extrema on a Closed Interval 1) Find the critical points of f on the interval [ a,b ]. 2) Find the relative extrema of f on (

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a,b ). 3) Find the absolute extrema of f on ( a,b ). Lecture 23 7 4) Find the absolute extrema of f on [ a,b ]. Theorem Lecture 23 8 To ﬁnd absolute extrema of function f on [ a,b ]: 1) Is f continuous on [ a,b ]? 2) 3) NOTE: Lecture 23 9 ex. Find the absolute extrema of f ( x ) = x 3-3 x 2 + 2 on [-1 , 1]. Lecture 23 10 ex. Find the relative extrema of f ( x ) = x 3-3 x 2 + 2. Lecture 23 11 ex. Find the absolute extrema of f ( x ) = x 2 + 18 x-3 on [2 , 12]. Lecture 23 12 ex. a) Find the absolute extrema of f ( x ) = x 2 + 18 x-3 on [-1 , 12]. b) Find the absolute extrema of f on (0 , 12]....
View Full Document

{[ snackBarMessage ]}

Page1 / 12

lecture23 - a,b 3 Find the absolute extrema of f on a,b...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online