2.6 - Student Lucas Rodrigues Instructor Gar Guy‘ton...

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Unformatted text preview: Student: Lucas Rodrigues Instructor: Gar Guy‘ton Assignment: Section 2.6 Date: lll'24l'10 Course: Guyton MA 160 Fall 2010 CRN Time: 12:19 PM 20746 8:40 AM Book: Bittinger: Calculus and Its Applications, 9e 1_ Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the production and sale of X items. If R(x) = 6x and C(x) = CLl'JO3x2 + 1.4x + 60, find each of the following. a) P(X) b) R(50), C(50), and P(50) 0) R’(x), C “(XL and P'(X) d) 11150), (3150), and P’(50) a) P(x) = |:| (Simplify your answer.) b) R(50) = $D C(50) = $lj P(50) = $lj c) R ’(x) = [:l (Simplify your answer.) c ’(x) = D (Simplify your answer.) P ’(x) = |:| (Simplify your answer.) (1) R’(50) = $I:I c ’(50) = $|:| P’(50)= $E] 2_ The average cost for a company to produce X units of a product is given by the function 16x + 1200 A(x) = —. Use A '(x) to estimate the change in average cost as production goes from 200 units to X 201 units. The change in average cost is approximately I:| dollars. Page 1 Student: Lucas Rodrigues Instructor: Gar Guyton Assignment: Section 2.6 Date: lli‘24f 10 Course: Guyton MA 160 Fall 2010 CRN Time: 12:19 PM 20746 8:40 AM Book: Bittinger: Calculus and Its Applications, 9e 3, Use the graph on the right to answer the following question. Alan earns $25,000 per year and is considering a second job that would earn him another $2000 annually. At what rate will his tax liability (the amount he must pay in taxes) change if he takes the extra job? Express your answer in tax dollars paid per dollar earned. Marginal tax rate (percentage) 0 50 100I I‘l50[ 200 250 I300 350 400 Annual income (in thousands of dollars) His tax liability will change by about $|:| per dollar earned. 4_ Find Ay and f ’(x)Ax. Fory=t(x)=6fx4, x= — 1.6, and Ax=0.1 Ay=|:| atx= - 1.6 and Ax=0.l (Do not round until the final answer. Then round to four decimal places as needed.) f ’(x)Ax=D atx= — 1.6 and Ax=0.1 (Do not round until the final answer. Then round to two decimal places as needed.) 5. Use Ay as f '(x)Ax to find a decimal approximation of the radical expression. W Value found by using Ay e: f ’(x) Ax. V 64.7 a D (Round to three decimal places as needed.) 6. Find dy. y=(3x3+3)3"2 dy = Ddx (Simplify your answer.) 7, Find dy. y=8x4+5x—3 dy=D Page 2...
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