Increasing and Decreasing Functions and the First Derivative

# Increasing and Decreasing Functions and the First...

This preview shows pages 1–11. Sign up to view the full content.

Increasing and Decreasing Functions and the First Derivative Test Section 3.3

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

View Full Document
decreasing constant increasing f ’ ’ (x) = 0 f ’ ’ (x) > 0 f ’ ’ (x) < 0
Test for Increasing & Decreasing Functions If f ‘ (x) > 0 for all x in (a,b), then f is increasing on [a,b]. If f ‘ (x) < 0 for all x in (a,b), then f is decreasing on [a,b]. If f ‘ (x) = 0 for all x in (a,b), then f is constant on [a,b].

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

View Full Document
Guidelines for Finding Intervals on Which a Function is Increasing or Decreasing Let f be continuous on (a,b) Find critical #s and use to determine test intervals. Determine the sign of f ‘ (x) at one test value in each of the intervals. Decide whether f is increasing or decreasing at each interval.( If f ‘ (x) + then increasing, if f ‘ (x < 0 then decreasing, If f ‘ (x) = 0 then constant.
A function is strictly monotonic on an interval if it is either increasing on the entire interval or decreasing on the entire interval. monotonic not monotonic

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

View Full Document
The First Derivative Test Let c be a critical number of a function

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 that is continuous on an open interval I containing c . If f is differentiable on the interval, except possibly at c , then f(c) can be classified as follows: If f (x) changes from negative to positive at c , then f(c) is a relative minimum of f . If f (x) changes from positive to negative at c , then f(c) is a relative maximum of f . When using the 1 st Derivative Test, be sure to consider the domain of the function. The undefined points must be used with other critical #s to determine the test intervals. relative minimums relative maximums neither rel. max. or min. Joke Time What do clowns do after April 30 th ? Ma-trix What do you get when you add 50 female pigs and 50 male deer? \$100,000 (100 sows an bucks) What do you call Calculus students who keep asking to go on a field trip to Cracker Barrel? Nothing. Theyre not going anywhere....
View Full Document

## This note was uploaded on 12/01/2011 for the course MATH 112 taught by Professor Jarvis during the Fall '08 term at BYU.

### Page1 / 11

Increasing and Decreasing Functions and the First...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online