The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 13{x^2} + 2x + 15$. Find the marginal revenue when $x = 7$.

We have, $R(x) = 13{x^2} + 26x + 15$ ….(i)

Differentiating (i) wr.t. $x$, we have.

Marginal revenue $= \cfrac{{dR}}{{dx}} = 13 \times 2x + 26 = 26x + 26$

Therefore, ${\left( {\cfrac{{dR}}{{dx}}} \right)_{x = 7}} = 26 \times 7 + 26 = 208$
$\Rightarrow$ Marginal revenue (when $x = 7$)$= Rs208$ .