F09e2s - Fall 2009 92.131 Exam 2 Solutions 1 2 a f x = sec 2 xe tan x b g x = tan x c s(t = t sin t 2 1 t 2 1 Consider the function f x = x 4 18 x

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Fall 2009 92.131 Exam 2 Solutions 92.131 Exam 2 Fall 2009 1) a) x e x x f tan 2 sec ) ( = b) x x g tan ) ( = c) 1 ) 1 sin( ) ( 2 2 + + = t t t t s 2) Consider the function 2 18 ) ( 2 4 + = x x x f . a) Find the intervals of increase or and decrease. ) 3 )( 3 ( 4 ) 9 ( 4 36 4 ) ( 2 3 + = = = x x x x x x x x f Function increases on ) , 3 ( ) 0 , 3 ( U . Function decreases on ) 3 , 0 ( ) 3 , ( U −∞ b) Find the local maximum and minimum values. Local mins of 79 at 3 ± = x . Local max of 2 at x = 0. c) Find the intervals of concavity and any points of inflection. ) 3 )( 3 ( 12 ) 3 ( 12 36 12 ) ( 2 2 + = = = x x x x x f . Concave up on ) , 3 ( ) 3 , ( −∞ U , concave down on ) 3 , 3 ( . Inflection points at ) 43 , 3 ( ± 3) Find the equation of the line tangent to the graph of ) sin( 2 y xy π = at the point ) 2 , 0 ( . Write your answer using slope-intercept form. Using Implicit Diff: )] sin( [ 2 y D xy D x x = or = + dx dy y x d y d x y ) cos( 2 2 , which at ) 2 , 0 ( becomes dx dy = 4 , and so 4 = = x d y d m . Tangent Line is ) 0 ( 4 2 = x y , or 2 4 + = x y . 4) Compute the second derivative of ) 3 cosh( ) ( 2 x e x f x = . ( ) 3 sinh( 3 ) 3 cosh( 2 ) ( 2 2 x e x e x f x x + = )] 3 cosh( 13 ) 3 sinh( 12 [ ) 3 cosh( 9 ) 3 sinh( 6 ) 3 sinh( 6 ) 3 cosh( 4 ) ( 2 2 2 2 2 x x e x e x e x e x e x f x x x x x + = + + +
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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