10. Consider the closed curve in the xy-plane given by: x3 + y = xy atx = 1 A. Show that = y -3x2 3y2 - x B. Find the linearization f (x) = L(x) of the function at x = 1. Use the equation to approximate f (1.1) 11. Use linearization to estimate the following and find the error of the approximation. A. (16.04) B. In (2.05) 12. The revenue for selling x items is R(x) = 1240x - 2x2 and the total cost C(x) = 650 + 8x. Write the profit function, (x) that gives the total profit earned. At what quantity will the profit be maximized? 13. The Cost, in dollars, of producing x gallons of interior paint is given by C(x) = 0.001x3 - 0.15x2 + 9x + 235. What is the instantaneous rate of change of the cost when 100 gallons are produced?14. A voice-activated monitor can be produced at a cost ofCL'r) = 1600 + 201: + 0.00113. A. Find the marginal cost function and use the function to estimate how fast the cost is going up if the company produces 1,000 monitors. B. Find the average cost function E (x) and evaluate C(IOOO). Explain the meaning in context to the production of the voice-activated monitors. C. Suppose the monitors sell for $35.00, write the prot function and use it to compute the marginal prot if 1,000 monitors are produced and sold. D. How many monitors should the company produce in order to maximize their prots. E. What is the maximum prot for your answer from part (D)