067Exam2asoln

067Exam2asoln - EXAM 2 Section October 12, 2006 NAME: Note...

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EXAM 2 Section October 12, 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. Tangent Line (6 points) Find an equation of the tangent line to the curve f ( x ) = 5 3 x 2 + 2 x + 2 at x = 1 . Solution: The slope of f ( x ) is given by the derivative: f ( x ) = 10 3 x + 2. So the slope of our desired tangent line is f ( 1) = 10 3 ( 1)+2 = 16 3 . Now f ( 1) = 5 3 ( 1) 2 +2( 1)+2 = 5 3 , so an equation of the desired tangent line is: y = 16 3 x + 11 3 . 1
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2. Derivatives (4 points each) Find the derivative of the function. You DO NOT need to SIMPLIFY your answer. (a)
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067Exam2asoln - EXAM 2 Section October 12, 2006 NAME: Note...

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