Q.The profit of a function $p(x)$ is maximum when :

Profit is maximised where its derivative is zero: $MR=MC$, i.e. $MC-MR=0$.

Profit is defined as revenue minus cost:

$P(x)=R(x)-C(x).$

For a maximum, set the first derivative to zero:

$P'(x)=R'(x)-C'(x)=0\;\Rightarrow\;MR-MC=0\;\Rightarrow\;MC-MR=0,$ …