1 / 7

70 likes | 206 Vues

Section 13.1 – 13.2 Increasing/Decreasing Functions and Relative Extrema. Facts. If f ’( x ) > 0 on an interval ( a,b ), then f ( x ) is increasing on ( a,b ). If f ’( x ) < 0 on an interval ( a,b ), then f ( x ) is decreasing on ( a,b ).

Télécharger la présentation
## Section 13.1 – 13.2 Increasing/Decreasing Functions and Relative Extrema

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Section 13.1 – 13.2Increasing/Decreasing Functions and**Relative Extrema**Facts**• If f ’(x) > 0 on an interval (a,b), then f (x) is increasing on (a,b). • If f ’(x) < 0 on an interval (a,b), then f (x) is decreasing on (a,b). • A number c for which f ’(c) = 0 or f ’(c) = undefined is called the critical number (critical value). Example: Find the intervals where the function is increasing/decreasing Definition:**Definition**• A function f has a relative maximum (or local max) at c if f (c) > f (x) for all x near c. • A function f has a relative minimum (or local min) at c if f (c) < f (x) for all x near c.**The First Derivative Test:**• If f ’(c) changes from + to – at c, then f has a local maximum at c. • If f ’(c) changes from – to + at c, then f has a local minimum at c. • No sign change at c means no local extremum (maximum or minimum)**How to find local max/min and interval of**increasing/decreasing: • Find all critical values by solving f’(x) = 0 or f ’(x) = undefined • Put all critical values on the number line and use test values to determine the sign of the derivative for each interval. • Determine the interval of increasing/decreasing based on the sign of derivative.**Examples**Find the intervals of increase/decrease and all local extrema.**Examples**A small company manufactures and sells bicycles. The production manager has determined that the cost and demand functions for q (q > 0) bicycles per week are where p is the price per bicycle. Find the (weekly) revenue function. Find the maximum weekly revenue. Find the maximum weekly profit. Find the price the company should charge to realize maximum profit.

More Related