# ch4rs - Name Calculus Answer each of the following...

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Name__________________________________________ Ch 4 Review Sheet Calculus Answer each of the following questions. 1. State the Extreme Value Theorem 2. State the Mean Value Theorem 3. Consider 4 3 3 2 + = x x y , at what values of x is there a max or a min? A point of inflection? 4. For what intervals is the function 3 12 3 + = x x y a. Increasing or decreasing? b. Concave up/down 5. What are the coordinates of max/min/points of inflection for the function in problem #4? 6. A function f has the derivative 3 2 ) 4 ( ) 2 ( ) ( ' + = x x x x f a. At what value(s) of x is there a maximum? b. At what value(s) of x is there a minimum? c. For what interval(s) is the function increasing? d. For what interval(s) is the function decreasing? 7. Consider the function x e x x y 2 3 ) 12 ( = a. For what values of x is there a relative maximum? b. For what values of x is there a relative minimum? c. For what values of x is there a point of inflection? 8. Mr. Brown is standing on a 18 foot ladder whose base is 6 feet from the wall of his house. If the bottom of the ladder is pulled out at a rate of 3 feet per second, then how fast is Mr. Brown moving down the wall when he is 1 foot above the ground? 9. A cylinder whose height is 5 in and whose radius is 8 in. is expanding such that the change in height is 3 in/min and the change in radius is –0.5 in/min.

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ch4rs - Name Calculus Answer each of the following...

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