calc notes lecture 14

calc notes lecture 14 - . At what x-values can f x '( )...

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Lecture Section Objectives Assignment 14 3.1 Increasing and Decreasing Functions 3.1: 3, 7, 9-33 odd, 37 Understanding Goals: 1. Understand the definition of increasing and decreasing functions and know how to test it. 2. Understand what critical number(s) of a function is and know how to find it. 3. Understand how to use critical number(s) to find the open intervals on which a function is increasing or decreasing. 4. Understand how to use increasing and decreasing functions to model and solve real-life problems. 1
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Example 1 : Show that the function f x x ( ) = 4 is decreasing on the open interval -∞ ,0 b g and increasing on the open interval 0, b g
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Unformatted text preview: . At what x-values can f x '( ) change signs? 2 3 Example 2 : Find the open intervals on which 3 2 3 ( ) 2 f x x x =-is increasing or decreasing. Interval Test Value Sign of f '( x ) Conclusion 4 Example 3 : Find the open intervals on which the function 4 2 1 ( ) x f x x + = is increasing or decreasing. 5 Example 4 : Find the critical numbers and the open intervals on which the function f x x x ( ) =-1 4 2 4 2 is increasing or decreasing. Example 5 : Find the critical numbers and the open intervals on which the function 3 2 1, 2 , x x y x x x x-+ =-+ is increasing or decreasing. 6 7...
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This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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calc notes lecture 14 - . At what x-values can f x '( )...

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