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Unformatted text preview: 1 Practice Test 2 1. Take the derivatives of the following functions: (a) f (x) = 4 3x3 + 2x + x (b) g(x) =
1 (x3 +2x2 +3x-1)4 2. Find the equation of the tangent line to F (x) = 2x2 - 4x + 1 at x = 3. 3. Find the second derivative of the following functions: (a) f (x) = (2x2 - 3x + 1)3/4 2x - 1 (b) g(x) = 3x + 2 4. Find the relative extrema of f (x) = 1-x2/3 . Classify the extrema as maxima or minima. 5. Sketch the graph of a function f (x) that is increasing on the intervals (-, 2) and (5, inf ty), decreasing on (2, 5) with a vertical asymtote at x = 2 and a left and right horizontal asymptote of y = 3. 6. Sketch the graph of f (x) = 3x4 - 2x2 . 7. Find the largest area enclosed by a fence with a perimeter of 60 feet.
1 8. Find all relative minima and maxima of F (x) = - 3 x3 + 6x2 - 11x - 50 on the interval [-3, 3]. Are any of the relative extrema absolute extrema and the same interval? 9. Does the function f (x) = real line? 10. Find limx 1 x2 have any absolute minima or maxima on the 11. A university is trying to set ticket prices for football games. If the tickets cost $18, average attendance is 40,000. For every $3 increase ticket price, 10,000 fewer people come. On average, each person spends $6 at the game on concessions and programs. Maximize the revenue of the university's football program. 12. Minimize Q(x, y) = 3x + y 3 where x2 + y 2 = 1. 13. HaHaTicToc sells 350 orchids per year. It costs $55 to store an orchid for one year. Each order costs $20 handling fee, plus $3 shipping per plant. How many times per year should the store order orchids, and in what lot size, in order to minimize inventory costs? See example Example 6, 2.5 4 + 2x + 3x2 . 1 - x - 5x2 ...
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This note was uploaded on 04/16/2008 for the course CALC 1304 taught by Professor Pruett during the Spring '08 term at Baylor.
- Spring '08