061Exam2asoln - EXAM 2 Section xxx March 2 2006 NAME Note...

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EXAM 2 Section xxx March 2, 2006 NAME: Note that to receive full credit on the short answer questions, relevant work and a correct answer must be shown. An incorrect answer with correct work for the problem shown can receive partial credit. A correct answer with no work shown can receive no credit. Good luck!! “On my honor, as a University of Colorado at Boulder student, I have neither given nor received unautho- rized assistance on this work.” YOUR SIGNATURE: 1. (6 points) Find the equation of the tangent line to the curve f ( x ) = (5 x 2 - 5 x - 2)( - 4 x + 1) at the point x = 0. Solution: f (0) = (5(0 2 ) - 5(0) - 2)( - 4(0) + 1) = - 2. Differentiating to find the slope at x = 0 gives f ( x ) = - 4(5 x 2 - 5 x - 2)+( - 4 x +1)(10 x - 5), so f (0) = - 4(5(0 2 ) - 5(0) - 2)+( - 4(0)+1)(10(0) - 5) = 3. So an equation of the line tangent to f ( x ) at x = 0 is y = 3 x - 2. 1
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2. Derivatives (2 points each) For each question, find the derivative of the indicated function and choose the single best answer. The problem will be graded as right or wrong, so no work is required to receive credit for these multiple-choice problems. Note that depending on method you use, some simplification may be required to find the correct equivalent choice.
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