We are going to find two nonnesat tive numbers whose sum is 40 and whose product is a maximum (A) Call the two numbers x and y. In terms of x and y, what is the quantity we are trying to maximize? Want to maximize xy (B) Your answer to part (A) should involve both x and y. Find an equation involving x and y, then solve it for y y =40x (C) Take Want to maximize x(40-x) your answer from part (B) and plug it into your answer from part (A). The result should be a formula in terms of only x. (D) What is the smallest value x can take on? (if there is no smallest value, enter "none") (E) What is the largest value x can take on? (if there is no largest value, enter "none") to maximize you function from part (C) over the interval defined by parts (D) andãE First, find the derivative of your function from part (C Derivative is 2x+40 (G) Find all x values where your answer to part (F) is zero or undefined Critical points occur atr none" if there is more than one critical point, enter a comma-separated list; if there are no critical points, enter OID Plug the povalbues ftom parts (tD).(B), ad (G) into your funsction from par (C) to dstermine which one produces the masximum valse. () Plug your answer from part (H) into your finction fiom part (B) to deternine the yevalue at which the masinum product occurs Maximum value occurs at 1-1 y-value at which the maximum product occurs. Maximum value occurs at y- J) If the sum of x and y is 40 and the product of x and y is a maximum, what are x and y? x.y are 20 20 (enter the values of x and y separated by commas, e.g., "2,8")