beams and bending

chihin098

A couple M will be applied to a beam of rectangular cross section from a log of circular cross section. determine the ratio d/b so that maximum stress will be minimum

σmax = M(d/2)/((1/12)bd³)
σmax = 6M/(b*d2)

and d² + b² = D²
D =diameter of the circle

but i can't find the ratio..
i know the answer of d/b is sqrt 2
how can i get the answer?
do i need differentiate?
if yes how should i do the differentiation??