exam2

# exam2 - –2 –1 1 2 3 x B –2 –1 1 2 y –3 –2 –1...

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MAT 3A – Winter 2008 Midterm II February 18, 2008 Name: Perm #: Schedule of discussion class: Instructions: The exam consists of 6 problems. You have 50 minutes to answer all questions. Please write full solutions, not just answers. Answers without justiﬁcation will get little or no partial credit. Show your work, explain your reasoning . You are not allowed to use any calcula- tors, books or notes. Good luck. Problem Max Score 1 12 2 10 3 8 4 10 5 10 6 10 Total 60 1

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1. Find the derivative of the functions. (a) (3 points) f ( x ) = x 2 + 3 x (b) (3 points) f ( x ) = sin x · cos x (c) (3 points) f ( x ) = e 2 + 7 2
(d) (3 points) f ( x ) = 10 x 1+ x 2. (10 points) Find f 0 (3) if f ( x ) = x + 1 using THE DEFINITION of the derivative . (0 point if use power rule) 3

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3. (8 points) For each of the 4 functions graphed below, ﬁnd the corresponding derivative function among the 8 choices (A-H, not just on the same row ), and put its letter in the corresponding box. 2 –4 –2 0 2 4 y –3 –2 –1 1 2 3 x A –4 –2 0 2 4 y –3
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Unformatted text preview: –2 –1 1 2 3 x B –2 –1 1 2 y –3 –2 –1 1 2 3 x 2 –3 –2 –1 1 2 3 y –3 –2 –1 1 2 3 x C –4 –3 –2 –1 1 2 3 4 y –3 –2 –1 1 2 3 x D –2 –1 1 2 y –3 –2 –1 1 2 3 x 2 –2 –1 1 2 y –3 –2 –1 1 2 3 x E –4 –2 2 4 y –3 –2 –1 1 2 3 x F –2 –1 1 2 y –3 –2 –1 1 2 3 x 2 –2 –1 1 2 y –3 –2 –1 1 2 3 x G –2 –1 1 2 y –3 –2 –1 1 2 3 x H –2 –1 1 2 y –3 –2 –1 1 2 3 x 4 4. (10 points) For what values of x does the graph of F ( x ) = x · e (-2 x ) have a horizontal tangent? 5. (10 points) Find the equation of the tangent line to the curve y = ln( x x ) at the point (3 , ln27). 6. (10 points) Use implicit diﬀerentiation to ﬁnd the equation of the tangent line to the curve x 2-2 xy + y 3 = 8 at the point (4 , 2). 5...
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## This note was uploaded on 04/07/2008 for the course MATH 3a taught by Professor Shu during the Winter '08 term at UCSB.

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exam2 - –2 –1 1 2 3 x B –2 –1 1 2 y –3 –2 –1...

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