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quizsoln7 - g y = 1 y g y = 1 y 2 Extra Credit(1 pt g y...

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Name:___________________________ Math 155 Quiz 7 10 October 2006 Instructions : This quiz is closed book and closed notes. You may NOT use a calculator. Label your answers and show all work. You need not simplify your answers. Find the derivatives of the following functions 1. f ( x ) = 1+ x - 2 1+ x 3 f '( x ) = (1+ x 3 )(- 2 x - 3 ) - (1+ x - 2 )(3 x 2 ) (1+ x 3 ) 2 2. g ( x ) = 1+ x e 2 x g '( x ) = ( e 2 x ) - (1+ x )(2 e 2 x ) ( e 2 x ) 2 3. f ( t ) = ( e t )( t e ) f '( t ) = ( e t )( et e - 1 ) + ( t e )( e t ) 4. Find the second derivative of g ( y ) = ln( y ) and discuss the concavity (curvature)
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Unformatted text preview: g '( y ) = 1 y g ''( y ) =- 1 y 2 Extra Credit (1 pt) g ''( y ) does not exist when y = 0, but for every other y, g ''( y ) is negative. Therefore, the function g ( y ) is concave down for all y except y = 0, when there is no concavity (curvature). Find the derivative of the following function f ( x ) = 4 xe-x 2 f '( x ) = 4 ( x )( e-x 2 )(- 2 x ) + ( e-x 2 )(1) [ ] (This uses the chain rule learned in 2.9)...
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