Homework 11

E b 5 and c 3 on the other hand to determine a we use

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Unformatted text preview: and c = 3. On the other hand, to determine a we use the fact that f (1) = a + b + c - Consequently, f (x) = 10 1 - 5x + 3x2 - x3 . 3 3 -4 -2 -2 -4 1 = 1. 3 3. 4 2 2 4 keywords: polynomial, local maximum 003 (part 1 of 1) 10 points 4. If f is a function on (-4, 4) having exactly two critical points and the sign of f , f are given in -4 f >0 f >0 f >0 f <0 -2 0 2 f <0 f >0 f <0 -2 4 2 2 -2 -4 4 Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken 4 2 2 -2 -4 -4 6. 4 2 -4 -2 -2 -4 Explanation: For the given sign chart f >0 f >0 f >0 f <0 -2 0 2 f <0 f >0 f <0 an inspection of the graphs shows that two of them fail to have exactly two critical points, leaving just four possible graphs for f . To distinguish among these we use the fact that (i) if f (x) > 0 on (a, b), then f (x) is increasing on (a, b), while (ii) if f (x) < 0 on (a, b), then f (x) is decreasing on (a, b), and that (iii) if f (x) > 0 on (a, b), then the graph is concave UP on (a, b), while (iv) if f (x) < 0 on (a, b), then...
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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.

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