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

Profit is maximum where marginal revenue equals marginal cost: $MR=MC$, i.e. $MC-MR=0$.

Profit is $p(x)=R(x)-C(x)$, where $R$ is total revenue and $C$ is total cost. For a maximum, the first derivative must vanish:

$p'(x) = R'(x) - C'(x) = MR - MC = 0 \;\Rightarrow\; MR = MC.$

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