1. The problem statement, all variables and given/known data Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. 2. Relevant equations 3. The attempt at a solution let a,b represent the two non negative numbers a=x b=30-x So, x^2+(30-x)^2=s, where s is the sum of their squares After expanding, the derivative is: s'=4x-60 let s'=0, then x=15. The interval for possible x values is 0≤x≤30. So let us check which value gives a maximum. s(15)=450 s(0)=900 s(30)=900 Therefore, the two non-negative numbers are 0 and 30. Is this right? I ask because the solution on a worksheet I have indicates that the two numbers are 15 and 15.