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11Arev6 - ucsc econ/ams 11b Review Questions 6 fall 2008...

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ucsc econ/ams 11 b fall 2008 Review Questions 6 Implicit differentiation and Taylor polynomials 1. Use implicit differentiation to find the indicated derivative at the given point. a. Find dy dx at the point (1 , 2) on the graph of the equation x 3 y +2 xy 3 - 4 x 2 y 2 = 2. b. Find du dv at the point (2 , e ) on the graph of the equation u 2 ln v + v 2 e - u = 5. 2. Find the equation of the tangent line to the graph of the equation x 3 y + 2 xy 3 - 4 x 2 y 2 = 4 at the point (2 , 1) on the graph. Note: You can use most of your work from problem 1a. here, but not all of it. 3. The demand equation for a firm’s product is given by p 2 q + 2 pq 3 / 2 + 3 q 2 = 42500 , where p is the price per unit for the firm’s product and q is the quantity demanded of the firm’s product. a. Find the price elasticity of demand for the firm’s product when p = 5 and q = 100. b. Estimate the percentage change in demand for the firm’s product, if they raise the price from p = 5 to p = 5 . 25. c. Use your answer to 3a to determine whether the firm’s revenue will increase or decrease if the firm raises the price? Explain you answer.
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