L18 - f ( x ) on each of the intervals, and use the Test...

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

Lecture 18: (Sec. 4.1) Increasing and Decreasing Functions ex. ex.

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

View Full Document
def. A function f is increasing on an in- terval ( a,b ) if for any two values x 1 and x 2 in ( a,b ), whenever x 1 < x 2 , then def. A function f is decreasing on an in- terval ( a,b ) if for any two values x 1 and x 2 in ( a,b ), whenever x 1 < x 2 , then NOTE: f is increasing (decreasing) at a point c if there is an interval ( a,b ) con- taining c so that f is increasing (decreasing) on ( a,b ). ex.
ex. For what intervals is f ( x ) = 4 - x 2 increasing and decreasing? NOTE: the graph of f 0 ( x ):

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

View Full Document
Theorem: Test for Increasing and De- creasing Functions Let f be diﬀerentiable on the interval ( a,b ). 1) 2) 3) NOTE:
ex. For what intervals is f ( x ) = x 2 / 3 in- creasing and decreasing? NOTE:

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

View Full Document
def. Suppose y = f ( x ) is deﬁned at x = c . Then c is a critical point(number) of f if 1) or 2) NOTE:
To Determine the intervals on which a continuous function is increasing or decreasing 1) Find the critical points of f and ﬁnd the open intervals determined by these points. 2) Determine the sign of

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: f ( x ) on each of the intervals, and use the Test for Increas-ing and Decreasing Functions to determine whether f is increasing or decreasing on each interval. ex. Given f ( x ) = x 3-3 2 x 2-6 x + 3. 1) Find all critical points of f . What are the coordinates of each point? 2) Find the open intervals on which f is increasing and decreasing. 3) Sketch the graph of f ( x ) = x 3-3 2 x 2-6 x + 3 ex. The position of a particle is given by the function s ( t ) = t 3-9 t 2 + 24 t where t is measured in minutes and s ( t ) is measured in yards. When is the particle moving for-ward? When is it moving backwards? ex. Consider the following graph of the derivative of a function f (so the graph is y = f ( x )). On what intervals is f in-creasing and decreasing?...
View Full 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 / 12

L18 - f ( x ) on each of the intervals, and use the Test...

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

View Full Document
Ask a homework question - tutors are online