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Unformatted text preview: Math 135 Exam 1 ReviewAnswers Fall 2010 1. Find f ( x ) for f ( x ) = 2 3 + x , using the definition of derivative. Answer: f ( x ) =- 2 (3+ x ) 2 2. Find the slope-intercept equation of the tangent line to the graph of y = 6 3 x- 1 x 2 at x = 1. Answer: y=4 x + 1 3. Assume the functions u ( x ) and v ( x ) are differentiable and that u ( x ) > 0 for all x . The following table gives the values of the functions and their derivatives at certain values of x : x u ( x ) v ( x ) u ( x ) v ( x ) 1 2- 1 3- 2 3 4 3- 2 1 4 3 2- 1- 3 (a) Let f ( x ) = x 4 u ( x ) + 3 v ( x ). Find f (1). Answer: f (1) = 5 (b) g ( x ) = v ( x ) u ( x ) . Find g (4). Answer: g (4) =- 7 / 9 (c) What can you say about the number and loca- tion of the solutions to the equation g ( x ) = 0? Justify your answer. Answer: Idea: apply the intermediate value the- orem which states that a continuous function g ( x ) over a closed bounded interval [ a,b ] such that g ( a ) g ( b ) < 0 has at least one zero between a and...
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