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19 Apr 2018

6. The parts of this question are independent of each other. (a) Let c = f(9) be a cost function where a > 0 is quantity. Assume when q = 4, the average cost is 80 and the marginal cost is 48. (i) Estimate c(5). MC C [3 points) (ii) Find the marginal average cost when q = 4. (4 points] (b) Verify that the equation 2 = 5.– 3 has a solution, r, in the interval (0,1). Use Newton's method to find the approximation 22 to r. Begin by selecting the appropriate starting value 21. Round your answer for X2 to three decimal places. [6 points)

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Sixta Kovacek
Sixta KovacekLv2
21 Apr 2018
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6. Assume the following throughout all of this question: a manufacturer finds that, when 8 units of a product are made, the total cost of production is $1,112 and $38.80 is the marginal cost. (a) Find the approximate cost to produce 9 units. Round your answer up to the nearest 1/100-th of a dollar. In the remainder of this question, assume the cost function for the product in part (a) and above has the special form C(q) = Aq+1 +K where A, B, and K are positive constants and q> 0 is the quantity produced. (b) If C) is the average cost and lim C(q) = 40, find A. [3 points) (c) Find the value of the constants B and K. [7 points)

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed

75 9. A marketing researcher has determined that when a product sells at a dollars per unit, the number of units sold per week is given by the function q = - + 80(5m - 2) where m>O is the total manufacturing cost in dollars per unit and m < x < 5m. 2 m (a) Find the profit function P(x) (in dollars per week) and simplify it. (5 points) (b) Use calculus to find the selling price x that maximizes weekly profit. Sufficiently justify your solution. [6 points] (c) Use your answer to part (b) to determine the manufacturing cost m that yields a maxi- mum weekly profit of 3, 455 dollars. [4 points)

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