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Exam 2 A solutions

# Exam 2 A solutions - Math 201 Exam 2 A Show all work to get...

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Math 201 Exam 2 A 04/08/08 Show all work to get full credit, each question is worth the same Name:__________________________________________________________________ 1. 2. Find dx dy at 2 1 , 1

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3. 4. 5.
6 . Graph 2 3 3 ) ( x x x f - = . Indicate coordinates of all local max/min points, and points of inflection. Your graph should show where the curve is concave up or concave down. The domain of f is all x -values. Now determine a sign chart for the first derivative, f ' : f '( x ) = 3 x 2 - 6 x = 3 x ( x - 2) = 0 for x =0 and x =2 . See the adjoining sign chart for the first derivative, f ' . Now determine a sign chart for the second derivative, f '' : f ''( x ) = 6 x - 6 = 6 ( x - 1) = 0

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for x =1 . See the adjoining sign chart for the second derivative, f '' . Now summarize the information from each sign chart. FROM f ' : f is ( ) for x <0 and x >2 ; f is ( ) for 0< x <2 ; f has a relative maximum at x =0 , y =0 ; f has a relative minimum at x =2 , y =-4 . FROM f '' : f is ( ) for x >1 ; f is ( ) for x <1 ; f has an inflection point at x =1 , y =-2 . OTHER INFORMATION ABOUT f : If x =0 , then y =0 so that y =0 is the y -intercept. If y =0 , then x 3 -3 x 2 = x 2 ( x -3)=0 so that x =0 and x
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Exam 2 A solutions - Math 201 Exam 2 A Show all work to get...

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