exam2_fa04 - f is decreasing. (b) Find the local maximum...

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Name: Section Number: TA Name: Section Time: Math 20A. Midterm Exam 2 November 17, 2004 You may use one page of notes, but no other assistance on this exam. Turn oF and put away your cell phone. Read each question carefully, answer each question completely, and show all of your work. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clari±cation. 1. (6 points) Find the linear approximation to f ( x ) = x 1 3 at x = 125 and use it to estimate (127) 1 3 . (Note: f (125) = 5.) # Score 1 2 3 4 5 Σ
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2. (6 points) Diferentiate the Following Functions; you need not simpliFy. (a) f ( x ) = x 2 + sin( x ) (b) g ( x ) = e 3 x cos(4 x ) (c) h ( x ) = [cos ( x )] x
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3. (6 points) Let f ( x ) = x + 1 x - 3 . The derivative of f is given by f 0 ( x ) = 1 - 1 ( x - 3) 2 . (a) Find the interval(s) on which f is increasing and the interval(s) on which
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Unformatted text preview: f is decreasing. (b) Find the local maximum and local minimum values of f . (c) Find the interval(s) on which the graph of f is concave upward and the interval(s) on which the graph of f is concave downward. 4. (6 points) Randall Cohn has a pool with the shape of an inverted cone which is 5 meters deep with a radius of 5 meters at the top (base). Randall Flls the pool with his garden hose at a rate of 0.1 cubic meters per minute. At what rate is the water depth increasing when the depth is 3 meters? (Note: The volume of a cone of height h and radius r is given by V = 1 3 r 2 h .) d = 5 r = 5 5. (6 points) Find the point(s) on the ellipse x 2 + xy + y 2 = 12 at which the corresponding tangent line is horizontal....
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exam2_fa04 - f is decreasing. (b) Find the local maximum...

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