1. [-/8 Points] DETAILS LARCALCET7 4.7.003. Find two positive numbers whose sum is 170 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Second Number, X Number Product, P 40 170 - 40 40(170 - 40) = 5,200 50 170 - 50 50(170 - 50) = 6,000 60 170 - 60 60(170 - 60) = 70 170 - 70 70(170 - 70) = 170 - 80 80(170 - 80) = 90 170 - 90 90(170 - 90) = (b) Write the product P as a function of X. P (x ) = (c) Use calculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-separated list.) (d) Use a graphing utility to graph the function in part (b) and verify the solution from the graph. 7220 160 8000 6000 7200 140 7180 120 6000 - 4000 7160 100 7140 80 4000 2000 7120 60 7100 2000 - 20 40 60 80 100 120 140 160 180 7080 20 7060 20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180 The solution appears to be at x = Need Help? Read It