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**Unformatted text preview: **MAC2233 Chapter 3 Review 1. Find the derivative of h ( x ) = ( x- 2)(2 x + 3) . 2. Find the derivative of f ( t ) = 3 t 4- 2 t + 5 t 2 . 3. Find the derivative of f ( x ) = 3 x 2- 4 x +2 x 2 +2 . 4. Find the equation of the tangent line to y = t 2 +2 t 4- 3 t 2 +1 at t = 0. 5. The total worldwide box-office receipts for a long-running movie are approximated by the function T ( x ) = 120 x 2 x 2 + 4 where T ( x ) is measured in millions of dollars and x is the number of years since the movies's release. How fast are the total receipts changing two years after its release? 6. Find the derivative of g ( u ) = u 5- 3 u 2 + 5 u- 6. 7. Find the derivative of h ( t ) = ( t 2- 6) 2 ( t 2 + 5) 3 . 8. Find the derivative of f ( x ) = x 2 +2 x 2 +1 . 9. Find the first, second, and third derivatives of f ( x ) =- 3 x 2 + 7 x- 2 . 10. Find the first and second derivatives of f ( x ) = x x 2 +1 . 11. The population of Americans age 55 yr and older as a percentage of the total population is approximated by the function f ( t ) = 10 . 72(0 . 9 t + 10) . 3 (0 t 20) where t is measured in years, with t = 0 corresponding to 2000. Compute f 00 (10) and interpret your result. 1 12. Use implicit differentiation to find y in the equation y 2 +2 xy + x 2 = 0 . 13. Use implicit differentiation to find y in the equation 1 x 3 + 1 y 3 = 5 x. 14. Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the equation 625 p 2- x 2 = 100 . If 25,000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 2 cents/carton/week, at what rate is the supply falling? 15. Two cars start at the same point. One travels north at a constant speed of 45 mph and the other travels east at a constant speed of 50 mph. At what rate is the distance between the cars increasing three hours later? 16. Given y = f ( x ) = 2 x + 1 determine the differential of the function....

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