Explanation :
From section AB
For equilibrium, $\sum{\mathrm M}_0=0$
$\begin{array}{l}\begin{array}{l}\mathrm M+\mathrm V\triangle\mathrm x+{\mathrm W}_\mathrm x\triangle_\mathrm x\frac{\triangle\mathrm x}2-\left(\mathrm M+\triangle\mathrm M\right)=0\\\triangle\mathrm M=\mathrm V\triangle\mathrm x+{\mathrm W}_\mathrm x\frac{\left(\triangle\mathrm x\right)}2^2\\\lim\limits_{\triangle x\rightarrow0}\frac{\triangle\mathrm M}{\triangle\mathrm x}=\lim\limits_{\triangle x\rightarrow0}\left(\mathrm V+{\mathrm W}_\mathrm x\frac{\triangle\mathrm x}2\right)\end{array}\\\Rightarrow\frac{\mathrm{dM}}{\mathrm{dx}}=\mathrm V\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...(\mathrm i)\end{array}$
and we know that for any function to be maximum or minimum it's differential should be equal to zero.
Hence from equation (i) for bending moment (M) to be maximum or minimum $\Rightarrow\frac{\mathrm{dM}}{\mathrm{dx}}=0$
Hence $\boxed{\frac{\mathrm{dM}}{\mathrm{dx}}=0}\Rightarrow\mathrm V=0$