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Unformatted text preview: a, b ). Problem 5. [20 Points] Construct an open box (it has a bottom but no lid), whose base is a rectangle that is twice as long as wide. What should its dimensions be (length, width, and height) if you are using 600 square centimeter of material and its volume is maximal? Problem 6. [35 Points] Discuss the function f ( x ) = ( x 24)( x + 1) . More specically: 1. Find the intercepts of f with the coordinate axes and the intervals on which the function f is positive, respectively negative. 2. Find the critical points of the function and the intervals on which f is increasing, respectively decreasing. 1 3. Use the values of f and f at x = 1 to get an approximate value for f (1 . 2). 4. Find the inection points and the intervals on which f is concave up, respectively concave down. 5. Find where the local minima and maxima of the function f occur. 6. Sketch the graph of f based on the information that you obtained. 2...
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 Spring '09
 Heiner
 Calculus

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