# The total revenue in Rupees received from the sale of $$x$$ units of a product is given by $R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $$x = 7$$.

Toolbox:
• If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
• $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$
• Marginal revenue is the rate of change of total revenue w.r.t the number of units sold.
Step 1:
Since the marginal revenue is the rate of change of total revenue w.r.t the number of units sold.
Marginal revenue (MR)=$\large\frac{dR}{dx}$
$\qquad\qquad\qquad\qquad=\large\frac{d}{dx}$$\big(13x^2+26x+15) Step 2: On differentiating we get, \large\frac{dR}{dx}$$=26x+26$
The marginal revenue when $x=7$
$\large\frac{dR}{dx}=$$26\times 7+26$
$\qquad=Rs.208$