Question

Find the number which, being added to its square, yields the least sum.

Answer 1

Let the number be $x$

Its square then will be $x^2$ and the required sum is

$S=x^2+x$

For maximum, we minima of this function, we differentiate it and find where its derivative becomes zero-

$⟹\frac{dS}{dx}=2x+1=0$

$⟹x=\frac{-1}{2}$

Hence, the required number is $\frac{-1}{2}$