Question

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

Answer 1

So we have
\[b = 50 - a\]\[f(a) = a^2 + (50 - a)^2\]

We are looking for the local min
\[f'(a) = 2a - (100 - 2a) = 4a - 100\]\[4a - 100 = 0\]\[a = 25\]

Answer 2

So \(a = 25\) and \(b = 25\)

Answer 3

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

Answer 4

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