1. The problem statement, all variables and given/known data The sum of two non-negative numbers is 20. Find the numbers (a) if the sum of their squares is to be as large as possible; (b) if the product of the square of one number and the cube of the other is as large as possible; (c) if one number plus the square root of the other is as large as possible. 2. Relevant equations 3. The attempt at a solution a. (x+y)(x+y)=x^2 +y^2 +2xy. x^2 +y^2=(x+y)^2 -2xy=400-2xy<=400 Maximum would be when 2xy=0, x=0, y=20. So is this fine or clear enough? Any better ideas? b. no idea. i can do it by calculus but why did my prof check at the endpoints ? c. no idea. i can do it by calculus but why did my prof check at the endpoints ?