Question

Divide 70 in to parts so that .Their product is maximum and sum of their square is minimum

Answer 1

Let 70 be divided into a and 70-a
we need to maximize
$a(70-a) = 70a - a^2$
and  minimize
$a^{2} + (70-a)^2$
So lets differentiate for local maximum
$70 - 2a = 0$
$a = 35$
So if we divide 70 as 35,35 we get product maximum and also we get sum of square minimum