test3sample - and use this information to sketch a graph....

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R McDougal Name: Math 151N 9 August 2005 Test III Sample Instructions: Answer each question as completely as you can; remember you must show all work for full credit. Partial credit may be given for incorrect answers with work; no credit will be given for incorrect answers without work. If you must use a theorem, be sure to verify that all of its hypotheses are satisfied. Please write as legibly as possible. For you to receive points, I must be able to read your solutions. If there is any danger of confusion, please circle your final answer. Please write all answers in the space provided. If you must continue your work in a dif- ferent location, please mark your work accordingly. Calculators are permitted subject to the restrictions stated in the syllabus. You may not consult books, notes or each other for this test. Good luck! Problem Value Score 1 25 2 13 3 12 4 12 5 13 6 25 total 100
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1. For the function f ( x ) = x 3 - 3 x - 7 find where f is increasing, decreasing, concave up, concave down, has critical points, inflection points, local maxes and local mins
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Unformatted text preview: and use this information to sketch a graph. (25 points). 2. Find inection point(s) and concavity for g ( x ) = 3 x 5-5 x 4 + 7 x- . (13 points). 3. Find two positive numbers x and y such that x 2 y is maximized. Be sure to verify that your result is a maximum and not a minimum. (12 points). 4. Find the (absolute) max and min of h ( x ) = x 3-6 x 2 + 9 x-4 on [-2 , 2]. (12 points). 5. Suppose farmer Bob (no relation to particle Bob from Test II) wants to claim a rectangular spot of land along a (perfectly straight) river. The river forms a natural edge of his property and Bob has 500 feet of fencing to mark o the rest of his property. What is the largest area Bob could claim? (13 points). 6. Find the largest total surface area (including top and bottom) of a cylinder inscribed in a cone with base radius 4 and height 24. (25 points)....
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This note was uploaded on 07/17/2008 for the course MATH 151 taught by Professor Any during the Summer '08 term at Ohio State.

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test3sample - and use this information to sketch a graph....

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