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Unformatted text preview: MAC2233 Chapter 4 Review 1. Find the intervals where the function g ( t ) = 2 t t 2 +1 is decreasing and increasing. 2. Use the First Derivative Test to find the relative extrema of the func tion f ( x ) = x 3 3 x 2 . 3. Sales in the Webhosting industry are projected to grow in accordance with the function f ( t ) = . 05 t 3 + 0 . 56 t 2 + 5 . 47 t + 7 . 5 (0 ≤ t ≤ 6) where f ( t ) is measured in billions of dollars and t is measured in years, with t = 0 corresponding to 1999. Find the intervals where f is increasing and decreasing. 4. For the function g ( x ) = x x +1 find any possible inflection points and the intervals where the function is concave up and concave down. 5. For the function g ( x ) = 2 x 3 3 x 2 +18 x 8 find any possible inflection points and the intervals where the function is concave up and concave down. 6. Use the Second Derivative Test to find the relative extrema of f ( x ) = 2 x 3 + 3 x 2 12 x 4 . 7. For the function f ( x ) = x 4 1 find: intervals upon which the function is increasing and decreasing; intervals upon which the function is concave upward and downward; local max and mins; inflection points; and vertical and horizontal asymptotes. Sketch the curve. 8. For the function f ( x ) = x 2 x 2 9 find: intervals upon which the function is increasing and decreasing; intervals upon which the function is concave upward and downward; local max and mins; inflection points; and vertical and horizontal asymptotes. Sketch the curve. 9. For the function f ( x ) = x 4 8 x 3 +18 x 2 +4 find: intervals upon which the function is increasing and decreasing; intervals upon which the function 1 is concave upward and downward; local max and mins; inflection points; and vertical and horizontal asymptotes. Sketch the curve. 10. Find the absolute max and min values of the function h ( p ) = p 1 p 2 +8 on the interval [ 3 , 3] . 11. An apartment complex has 100 twobedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by P ( x ) = 10 x 2 + 1760 x 50 , 000 . To maximize the the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable? 12. Philip, the proprietor of a vineyard estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $ 5 per bottle. But if more than 10,000 bottles were purchase, then the profit/bottle for the entire lot would drop by $ 0.0002 for each additional bottle sold. Assuming that at least 10,000 bottles of wine are produced and sold, what is the maximum profit? 13. If an open box (the box has no top) has a square base and a volume of 108 cubic inches and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction....
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 Spring '08
 Smith
 Calculus, Derivative, Mathematical analysis, Convex function, Concave function

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