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Sheet (7) solution

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

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1 Math 103 Class Work Sheet (7) Solution [1] (a) 3 3 ) ( 3 + - = x x x f Domain ) , ( -∞ y-intercept ) 3 , 0 ( x-intercept 0 3 3 3 = + - x x (difficult) Symmetry No Asymptotes No ) ( ' x f 3 3 ) ( ' 2 - = x x f Critical Points 1 0 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 , 0 (

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2 (b) 2 4 2 ) ( x x x f - = Domain ) , ( -∞ y-intercept ) 0 , 0 ( x-intercept ) 0 , 2 ( ), 0 , 2 ( ), 0 , 0 ( 2 , 2 , 0 0 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 , 0 0 4 4 ) ( ' 3 ± = = - = x x x x f Increasing & Decreasing intervals Local max. & Local min. ) 1 , 1 ( & ) 1 , 1 ( - - - are local max. points ) 0 , 0 ( is local minimum point ) ( ' ' x f 4 12 ) ( ' ' 2 - = x x f Concavity Inflection points - - 556 . 0 , 3 1 & 556 . 0 , 3 1
3 (c) 2 5 2 ) ( - = x x x f Domain ) , ( -∞ y-intercept ) 0 , 0 ( x-intercept ) 0 , 10 ( ), 0 , 0 ( 10 , 0 0 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 0 5 2 3 5 2 ) ( ' = = - - = x x x x f Increasing & Decreasing intervals Local max. & Local min. 037 . 37 , 3 10 is local maximum ) 0 , 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

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4 (d) π 2 0 sin ) ( + = x x x x f Domain ] 2 , 0 [ π y-intercept ) 0 , 0 ( x-intercept 0 sin = + x x Symmetry No Asymptotes No ) ( ' x f x x f cos 1 ) ( ' + = Critical Points π = = + = x x x f 0 cos 1 ) ( ' Increasing & Decreasing intervals Local max. & Local min. No ) ( ' ' x f x x f sin ) ( ' ' - = Concavity Inflection points ) , ( π π
5 (e) 2 8 ) ( x x x f - = Domain 2 2 | | 8 0 8 2 2 - x x x ] 2 2 , 2 2 [ - y-intercept ) 0 , 0 ( x-intercept ) 0 , 2 2 ( ), 0 , 2 2 ( ), 0 , 0 ( 2 2 , 0 0 8 2 - ± = = - x x x Symmetry - = - - = - - - = - ) ( 8 ) ( 8 ) ( 2 2 x f x x x x x f odd function Asymptotes No ) ( ' x

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