solhw7new[1] - Homework#7 Section 3.4 2 2 2 3 2 when cos 2...

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Unformatted text preview: Homework #7 Section 3.4 2. ) 2 , ( 2 3 , 2 when cos 2 ) ( sin 2 1 ) ( cos 2 ) ( π π π on x x x f x x f x x x f = =- = ′ ′ ⇒- = ′ ⇒ + = Since it is all similar, I will do only the first period, that is, on ) 2 , ( π Please graph the second derivative function x x f cos 2 ) (- = ′ ′ with your graphing calculator and verify the signs on the table below. Intervals ) 2 , ( π ) 2 3 , 2 ( π π ) 2 , 2 3 ( π π Sign of f ′ ′- +- Concavity of f down up down 3. 2 2 ) 4 ( ) 2 ( 8 1 ) (- +- = x x x f ) 4 ( ) 2 ( 4 1 ) 4 )( 2 ( 4 1 ) 4 ( 2 ) 2 ( 8 1 ) 4 )( 2 ( 2 8 1 ) ( 2 2 2 2- +-- +- =- ⋅ + ⋅-- + ⋅- = ′ x x x x x x x x x f Factor the common factor: ) 4 )( 2 ( 4 1- +- x x [ ] 4 , 2 when ) 4 )( 2 ( 2 3 ) 6 )( 4 )( 2 ( 4 1 ) 2 ( 4 ) 4 )( 2 ( 4 1 ) (- = =- + =-- +- = +--- +- = ′ x x x x x x x x x x f Now the second derivative: 9 ) 1 2 ( 3 ) 2 ( ) 1 ( 3 ) 2 2 ( 2 3 ) 2 4 ( 2 3 ) 2 ( 2 3 ) 4 ( 2 3 ) ( <- =-- =- ′ ′- =- = + +- = + +- = ′ ′ f x x x x x x x f Which implies...
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This note was uploaded on 04/07/2008 for the course COMM 1001 taught by Professor Burner during the Fall '08 term at University of Houston.

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solhw7new[1] - Homework#7 Section 3.4 2 2 2 3 2 when cos 2...

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