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Unformatted text preview: P of f the xaxis and yaxis have been omitted, but the point P = (1, 1) on the graph has been included. Use calculus to determine which of the following f could be. 1 2 1. f (x) =  + 3x  x2  x3 3 3 4 1 2. f (x) =  + 5x  3x2 + x3 3 3 3. f (x) = 10 1  5x + 3x2  x3 correct 3 3 1. none of them 2. A and B only 3. B and C only correct 4. all of them 5. A and C only 6. A only 7. B only 8. C only 8 1 4. f (x) =  + 3x + x2  x3 3 3 Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken 8 1 5. f (x) =  3x + x2 + x3 3 3 6. f (x) = 1 14  3x  x2 + x3 3 3 2 decide which of the following could be the graph of f . 1. 4 2 4 2 2 4 2 4 Explanation: From the graph, f (x)  as x . Of the six given choices, therefore, f must have the form 1 f (x) = a + bx + cx  x3 3
2 with {b, c} being one of {3, 1}, Now f (x) = b + 2cx  x2 , f (x) = 2(c  x) . 4 2 2 4 2 4 {3, 1}, {5, 3} . 2. 4 2 Since the graph has a local miminum at x = 1, it follows that b + 2c  1 = 0, c1 > 0 , i.e., b = 5...
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This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.
 Spring '08
 schultz
 Differential Calculus

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