Question

If $a$ and $b$ are two parts of $8$ such that sum of their cubes is the least possible then $ab$ is equal to

Answer 1

$a+b=8f\left(a\right)=a^3+{(8-a)}^{3}f\left(a\right)=512+24a^2-192a{f}^{\prime }\left(a\right)=0forminoff\left(a\right)48a=192a=4sob=4soa.b=16$