Worksheet_2 - B us 14B Online Worksheet#2 Show all work on...

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Unformatted text preview: B us 14B - Online Worksheet #2 Show all work on answer sheet. Then submit as an email attachment or bring to R308d (or R201) by deadline. Find all points where the function is discontinuous. 10) 1) Suppose the cost of producing x items is given by C(x) = 3600 - x 3 and the revenue made on the sale of x items is R(x) = 300x - 12x 2 . a) Find the number of items which serves as a break- even point. b) Find quantity to maximize profit. c) GRAPH/Label CRP Graph this rational function, label the vertical and horizaontal asymptotes. 5x + 2 2) y = x+3 Find the average rate of change for the function over the given interval. 11) y = 6 x 3 - 2x 2 - 5 b etween x = 2 and x = 7 Find the derivative. (Section 12.1) 12) y = 17x - 2 - 2x 3 - 9x 3) A college student invests $7000 in an account paying 8 % per year compounded annually. In how many years will the amount at least quadruple? 13) f(x) = 9x 7/5 - 5x2 + 104 14) g(x) = 4 x 5 + x4 - 7x 2 + 3, find g'(- 1 ) Find the limit. If possible, factor first. x 2 - 100 4) lim x 10 x - 10 5) 6) x x lim lim To find the max or min "x" value, take the first derivative of the function, set it equal to zero, and solve for "x". 15) If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a x certain city, where p(x) = 111 . How many 12 x 2 + 7 x - 30 x2 - 9 3 1 1 x+3 3 0 x candy bars must be sold to maximize revenue? (First, simplify fraction.) 16) A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Find the limit as h approaches zero. lim (x + h)3 - x3 7) h 0 h 17) S(x) = - x 3 + 6x2 + 288x + 4000, 4 x 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon. 8) Find the interest earned on $ 10,000 invested for 6 years at 6.9% interest compounded quarterly. Find all values where the function is discontinuous (the denominator can never equal zero) and graph (factor first!). x- 5 9) = 2 - 17x+ 10) (3 x 18) A piece of molding 155 cm long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area? 1 Answers for Worksheet #2 1. See the pencasts for two problems similar to this one. Courtesy of Diane – one of your classmates! 13. f(x) = 9x7/5–5x2+104 f’(x) = x2/5-10x 7. Revenue is maximized at 5000 units. Profit is maximized at 4000 units. 14. g(x) = 4x5+x4-7x2+3 g’(x) = 20x4+4x3-14x g’(-1) = 20(-1)4+4(-1)3-14(-1) = 20-4+14 = 30 2. Graph…. Vert asympt: x = -3; Horiz asymp: y = 5 15 Vert Asympt 8. P = $10,000, t = 6, r = 6.9%, m = 4 A = $15,075.26 (TI-84 Solver) Total interest earned: $15,075.26 – 10,000 = $5,075.26 15. 10 Horiz Asympt 5 To maximize revenue, sell 666,000 candy bars. 0 -15 -12 -9 -6 -3 -5 0 3 6 9 12 3. P = $7,000, r = 8%, m = 1, A = 4 X $7,000 = $28,000 t $28000 = $7000(1 + 0.08) t 4 = 1(1.08) t= = 18.01 It takes a little over 18 years to quadruple, but since interest is only compounded annually, it will take 19 years to get over 4 times. 4. 5. 6. 16. 9. Discontinuous at x = 2/3, 5; VA: x = 2/3; HA: y = 0 -3 -2 4 3 2 1 0 -1 -1 -2 -3 -4 Surface Area S’ 0 1 2 3 4 5 6 10. Discontinuous at x = -2, x = 0 (vert asymptote), x = 2; (also a horiz asymptote at y = 0) The width of the box to minimize surface area is 3.11ft. 17. The temperature to maximize the number of salmon is 12°C. 11. f(7) = 6(7)3–2(7)2-5 = 1955 f(2) = 6(2)3-2(2)2-5 = 35 ave rate of change = 12. y = 17x-2-2x3-9x y’ = -34x-3-6x2-9 18. The dimensions to maximize the frame area are 38.75cm X 38.75cm. ...
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This note was uploaded on 11/13/2011 for the course ACCT 101 taught by Professor Dontknow during the Spring '08 term at Central Washington University.

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