10FallHwk08

10FallHwk08 - Math 2413 The Shape of a Graph, Part II...

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Math 2413 Homework Set 8 10 Points The Shape of a Graph, Part II 1. Determine the intervals where ( ) 5 43 11 56 5 1 29 f xxxxx =+--- is concave up and concave down. What are the inflection points for this function? 2. Use ( ) 654 5 1 2 60 h xxxx =-- for this problem. (a) What are the intervals of increase/decrease for this function? (b) What are the relative extrema of this function? (c) Find the intervals of concave up/concave down for this function. (d) Find all the inflection points for this function. (e) Use the information above to sketch the graph of this function. 3. Suppose that you know that the critical points of ( ) fx are 7 x =- , 4 x , and 1 x and that the second derivative of ( ) 32 4 3 9 10 2 67 f xx ¢¢ =+++ . If possible, classify the critical points. If it is not possible clearly explain why it is not possible. The Mean Value Theorem 4. Verify that ( ) 2 7 10 g xx xx ++ satisfies the conditions of the Mean Value Theorem on [-2, 1] and find all values of c that satisfy the conclusion of the Mean Value Theorem on [-2, 1].
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10FallHwk08 - Math 2413 The Shape of a Graph, Part II...

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