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Unformatted text preview: Math 124 Quiz 4 Sept. 29, 2006 SOLUTIONS 1) [4 points] Find the derivatives of the following functions with respect to the indicated variables. There is no need to simply answers. Do NOT use the product or quotient rules here. (a) f ( x ) =- 3 x 1 3 + 2- x , with respect to x (b) g ( t ) = 2 t 4- 5 t + 7 t , with respect to t (c) w ( z ) = az 2 + z + 1 z , with respect to z (d) h ( r ) = a r b , with respect to r (e) g ( a ) = e a + a e , with respect to a Solutions: (a) f ( x ) =- x- 2 3- 1 2 x- 1 2 (b) g ( t ) = 8 t 3- 5 2 t- 1 2- 7 t- 2 (c) First rewrite w ( z ) = az + 1 + z- 1 . Then w ( z ) = a- z- 2 (d) Rewrite h ( r ) = ( 1 b ) a r . Treat 1 b as a constant. Then h ( r ) = 1 b a r ln a (e) Here remember to treat a as the variable. Then g ( a ) = e a + ea e- 1 , since the derivative of e a is itself and a e is a power function. 2) [2 points] Let f ( x ) = 4 x 2 + 3 e x . Find an equation of the tangent line through f at x = 1. Do not use decimal approximations in your answer, i.e. leave answers in exact form. Theres no need to reduce oruse decimal approximations in your answer, i....
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