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exam2_fa03

# exam2_fa03 - points(e Use the information above to sketch...

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Name: Section Number: TA Name: Section Time: Math 20A. Midterm Exam 2 November 18, 2003 You may use one page of notes, but no other assistance on this exam. 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 clarification. 1. (5 points) Differentiate each function (a) x x + 2 (b) ln( x ) cos ( e x ) # Score 1 2 3 4 5 Σ

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2. (10 points) Let h ( x ) = x 3 - 3 x + 1. (a) Find the intervals on which h is increasing and decreasing. (b) Find the local maxima and local minima of h and the points where they occur. (c) Find the absolute maximum and absolute minimum of h over the interval [ - 2 , 2] and the points where they occur.
(d) Find the intervals on which the graph of h is concave up and concave down and find the inflection

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Unformatted text preview: points. (e) Use the information above to sketch the graph of h .-2-1 1 2-6-4-2 2 4 6 3. (5 points) Find an equation for the tangent line to the graph of x 2 + xy-y 2 = 1 at the point (-2 ,-3). 4. (5 points) Find the linear approximation to f ( x ) = e 3 x at x = 0, and use it to estimate f (0 . 1). 5. (5 points) A ladder stands in the middle of a room, forming an isosceles triangle whose base is on the Foor and whose equal sides measure 13 feet each. Suddenly, the brace joining the two sides of the ladder breaks and it collapses, always forming an isosceles triangle. How fast is the base of this triangle changing when the top of the ladder is 5 feet above the ground and dropping at 16 feet/second?...
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