Homework 5.4

question 3

x A company manufactures mountain bikes. The research department produced the marginal cost function C'(x)= 200 E' OSXSQOO, where C'(x) is in dollars and x is the number of bikes produced per month. Compute the increase in cost going lrom a production level of 450 bikes per month to 720 bikes per month. Set up a denite integral and evaluate it. The increase in cost is $ Calculate the definite integral by referring to the figure with the indicated areas. + [f ( x ) dx A b X a B D Area A = 1.502 Area C = 5.19 Area B = 2.495 Area D = 1.7 . . . C f ( x ) d x = aThe total cost (in dollars) of manufacturing x auto body frames is C(x) = 70,000 + 100x. (A) Find the average cost per unit if 700 frames are produced. [Hint: Recall that 5(x) is the average cost per unit] (B) Find the average value of the cost function over the interval [0,700]. (O) Discuss the difference between parts (A) and (B). E> (A) The average cost per unit if 700 frames are produced is $|:|. Calculate the indicated Riemann sum S5, for the function f(x) = 16 -5x. Partition [ - 5,5] into five subintervals of equal length, and for each subinterval [Xk - 1,XK], let Ck = (Xk-1 + Xk) /2. S5 =Answer the following questions about F(x) = 9x+ 130. (A) Calculate the change in F(x) from x =14 to x = 19. (B) Graph F'(x) and use geometric formulas to calculate the area between the graph of F'(x) and the xaxis from x = 14 to x = 19. (C) Verify that your answers from (A) and (B) are equal, as guaranteed by the fundamental theorem of calculus. <:> (A) Calculate the change in F(x) from x =14 to x = 19. The change is D. (Simplify your answer.) Area A = 1,316 Calculate the definite integral f(x) dx by referring to the figure on the right with the indicated areas. Area B = 2,380 Area C = 3,022 Ab C d x a B C D Area D = 1,760 f ( x ) dx = [ (Simplify your answer.)