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Unformatted text preview: Exercises UF Calculus Set 24 1. Given the graph of f ( x ) shown, determine the following: the intervals on which f is increas ing/decreasing; the intervals on which f is concave up/down; the critical numbers, the local extrema, and inflection points for f . 2. Suppose that the graph from Exercise 1 is actually the derivative g of a continuous function g . Determine the following: the intervals on which g is increasing/decreasing; the intervals on which g is concave up/down; the critical numbers, the local extrema, and inflection points for g . Draw a rough sketch of g , remembering that it is assumed to be continuous. 3. Detemine the intervals on which the functions are increasing/decreasing. Identify all local extrema with first derivative test. (a) f ( x ) = 2 3 x 1 + 2 x (b) f ( x ) = x 2 + 8 ln( x ) 10 x (c) f ( x ) = 1 1 + xe x (d) f ( x ) = x 4 √ x (e) f ( x ) = x 2 / 3 1 + x 2 (f) f ( x ) = e x (5 x ) 2 (g) f ( x ) = sin( x ) 2 + cos( x ) (h) f ( x ) = 2 ln( x ) 5 arctan(...
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This note was uploaded on 05/17/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.
 Spring '08
 ALL
 Calculus, Geometry

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