QPaperGen

The total revenue (in rupees) from selling \(x\) units of a product is given by:
\[R(x) = 13x^2 + 26x + 15\]

We are asked to find the marginal revenue when \(x = 7\).\[\]

Marginal revenue is the rate of change of total revenue with respect to the number of units sold, i.e.,

\(MR = \dfrac{dR}{dx}\)
\[\]

Differentiate \(R(x)\):

\[\dfrac{dR}{dx} = 13 \cdot 2x + 26 = 26x + 26\]

Now substitute \(x = 7\):

\[MR = 26 \cdot 7 + 26 = 182 + 26 = 208\]

Final Answer:
The marginal revenue when \(x = 7\) is Rs. 208