(1) Find the differentialdyof the given function. (Use "dx" fordx.)

y=6x²?8

dy = _________

(2) Find two positive numbers whose sum is210and whose product is a maximum.

(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)

(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 60 210 - 60 60(210 - 60) = 9,000 70 210 - 70 70(210 - 70) = 9,800 80 210 - 80 80(210 - 80) = 90 210 - 90 90(210 - 90) = 100 210 - 100 100(210 - 100) = 110 210 - 110 110(210 - 110) = (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. 12080 18000 1 1000 10080 150 10950 600 6000 4000 100 10900 4000 200 50 2000 10850 10.0 150 200 O 50 150 200 -2000 50 100 150 206 300 The solution appears to be at x =