Please explain how to do it as well as result:
The sum of two non-negative numbers is 20. Find the numbers If the sum of their squares is as large as possible; as small as possible. This is optimization.

Question

Please explain how to do it as well as result: 
The sum of two non-negative numbers is 20. Find the numbers If the sum of their squares is as large as possible; as small as possible. This is optimization.

anonymous · Answer

if the sum is $20$ and one is say $x$ then the other is $20-x$ maximize 
$$f(x)=x^2+(20-x)^2$$

anonymous · Answer

not sure what you are supposed to use, but 
$$f(x)=2 x^2-40 x+400$$ is a quadratic, min is at the vertex