Sheet (7) solution - 1 Math 103 Class Work Sheet (7)...

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Unformatted text preview: 1 Math 103 Class Work Sheet (7) Solution [1] (a) 3 3 ) ( 3 +- = x x x f Domain ) , ( ∞-∞ y-intercept ) 3 , ( x-intercept 3 3 3 = +- x x (difficult) Symmetry No Asymptotes No ) ( ' x f 3 3 ) ( ' 2- = x x f Critical Points 1 3 3 ) ( ' 2 ± = =- = x x x f Increasing & Decreasing intervals Local max. & Local min. ) 5 , 1 (- is local maximum point ) 1 , 1 ( is local minimum point ) ( ' ' x f x x f 6 ) ( ' ' = Concavity Inflection points ) 3 , ( 2 (b) 2 4 2 ) ( x x x f- = Domain ) , ( ∞-∞ y-intercept ) , ( x-intercept ) , 2 ( ), , 2 ( ), , ( 2 , 2 , 2 2 4-- = ⇒ =- x x x Symmetry ⇒ =- =--- =- ) ( 2 ) ( 2 ) ( ) ( 2 4 2 4 x f x x x x x f even Asymptotes No ) ( ' x f x x x f 4 4 ) ( ' 3- = Critical Points 1 , 4 4 ) ( ' 3 ± = ⇒ =- = x x x x f Increasing & Decreasing intervals Local max. & Local min. ) 1 , 1 ( & ) 1 , 1 (--- are local max. points ) , ( is local minimum point ) ( ' ' x f 4 12 ) ( ' ' 2- = x x f Concavity Inflection points                -- 556 . , 3 1 & 556 . , 3 1 3 (c) 2 5 2 ) (      - = x x x f Domain ) , ( ∞-∞ y-intercept ) , ( x-intercept ) , 10 ( ), , ( 10 , 5 2 2 ⇒ = ⇒ =      - x x x Symmetry No Asymptotes No ) ( ' x f      -      - =      - +      - = 5 2 3 5 2 5 2 5 2 ) ( ' 2 2 x x x x x x f Critical Points 3 10 , 10 5 2 3 5 2 ) ( ' = ⇒ =      -      - = x x x x f Increasing & Decreasing intervals Local max. & Local min.       037 . 37 , 3 10 is local maximum ) , 10 ( is local minimum ) ( ' ' x f      - +      - = 5 2 2 3 5 2 3 2 1 ) ( ' ' x x x f Concavity Inflection points       519 . 18 , 3 20 4 (d) π 2 sin ) ( ≤ ≤ + = x x x x f Domain ] 2 , [ π y-intercept ) , ( x-intercept sin = + x x Symmetry No Asymptotes No ) ( ' x f x x f cos 1 ) ( ' + = Critical Points π = = + = x x x f cos 1 ) ( ' Increasing & Decreasing intervals Local max. & Local min....
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This note was uploaded on 01/09/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Spring '09 term at German University in Cairo.

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Sheet (7) solution - 1 Math 103 Class Work Sheet (7)...

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