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Math+1550+Homework+5 - e. Identify any local extrema of the...

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1Math 1550 Homework 5 Fall 2005 1. Use the graph of the function to answer the following. a. What is domain and range of the function? b. Over what intervals is the function increasing? c. Over what intervals is the function decreasing? d. What is the absolute maximum and minimum for the function? e. What are the local maxima for the function? (Give as f(a)=d) f. What are the local minima for the function? (Give as f(a)=b) g. Over what intervals is the function concave upward? h. Over what intervals is the function concave downward? i. What are the coordinates of any inflection points? 2. Given 4 3 8 200 ) ( x x x f + + = a. Find the critical numbers for this function. b. Find the absolute extrema over [-10, 1]. c. Over what intervals is the function increasing? d. Over what intervals is the function decreasing?
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Unformatted text preview: e. Identify any local extrema of the function. f. Over what intervals is the function concave upward? g. Over what intervals is the function concave downward? h. Give the coordinates of any inflection points. 3. Suppose that ) ( x f is continuous on [0,4], 1 ) ( = f , and 5 ) ( 2 x f for all x in (0,4). Show that 21 ) 4 ( 9 f . 4. Sketch the graph of a continuous function satisfying: f(0)=2; f(2)=f(-2)=1;f (0)=0; f (x)> 0 if x < 0; f (x) < 0 if x> 0; f (x) > 0 if |x| < 2; f (x) > 0 if |x| > 2. 5. Given f(x) = cos x + sin x. Sketch a graph of f(x) indicating all relative extrema and inflection points. Show all work....
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This note was uploaded on 04/10/2008 for the course ANTH 101 taught by Professor Zhang during the Spring '08 term at Tulane.

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