Find two positive integers whose sum is 50 and the sum of their square is a minimum. I need solution please. :) Thanks!

Question

anonymous · Answer

So we have
$$b = 50 - a$$$$f(a) = a^2 + (50 - a)^2$$

We are looking for the local min
$$f'(a) = 2a - (100 - 2a) = 4a - 100$$$$4a - 100 = 0$$$$a = 25$$

anonymous · Answer

So $a = 25$ and $b = 25$

anonymous · Answer

How did it became 100-2a? i think 50 squared is 2500, so how did that come up to 100?

anonymous · Answer

I'm assuming this is a calculus course is it not? We are talking about the derivative not the function.