Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when x = a. c. Interpret the values obtained in part (b). C(x) =0.01x#+0.7x7 + 50x + 110, 05xs 1500, a = 500 a. The average cost function is C(x) = [. The marginal cost is function is C'(x) =_ b. The average cost when x = a is $ . (Round to two decimal places as needed.) The marginal cost when x = a is $ . (Round to two decimal places as needed.) c. Choose the correct interpretation of the average cost when x = a. O A. The cost of producing 500 items is about $1,600.22. O B. The average cost per item is about $2,900.22 when 500 items are produced. O C. The cost of producing the 501st item is about $8,250.00. O D. The cost of producing the 501st item is about $2,058.01. Choose the correct interpretation of the marginal cost when x = a. O A. The average cost per item is about $2,900.22 when 500 items are produced O B. The cost of producing the 501st item is about $8,250.00. O C. The cost of producing 500 items is about $1,600.22. O D. The cost of producing 501 items is about $758.01.For the following composite function, find an inner function u = g(x) and an outer function y = f (u) such that y = f(g(x)). Then calculate dx y= 16+ 5x Select the correct choice below and fill in the answer box to complete your choice. dy d d O A. dx du (6 + 5u) . dx (VX ) = dy d d O B. E dx du ( vu) . dx (6+ 5x) dy d d O C. dx du ( vu) . (5x) = dx dy d OD. E dx du (u) dx (6 + 5x) =dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point. 4 x - 3vy = 13; (16,1) dy a. dx b. The slope of the curve at the point (16,1) is (Simplify your answer.)