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# The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 3{x^2} + 36x + 5$. The marginal revenue, when $x = 15$ is,(a) $116$(b) $96$(c) $90$(d) $126$  Answer Verified
Hint: Differentiate the given equation carefully without missing any term in between. ALSO Marginal revenue is the derivative of total revenue with respect to demand.

We have the given equation as,$R(x) = 3{x^2} + 36x + 5$
… (1)
Now, we know that,
⇒Marginal revenue $= \dfrac{{dR(x)}}{{dx}}$
Therefore, differentiating equation (1) with respect to $x$ , we get,
$\dfrac{{dR(x)}}{{dx}} = 3\dfrac{{d{x^2}}}{{dx}} + 36\dfrac{{dx}}{{dx}} + 5\dfrac{{d1}}{{dx}}$
$\Rightarrow \dfrac{{dR(x)}}{{dx}} = 3(2x) + 36x + 0$
$\Rightarrow \dfrac{{dR(x)}}{{dx}} = 6x + 36$
It is given in the question that we have to calculate the marginal revenue at $x = 15$
Therefore, Marginal revenue $= 6(15) + 36$
$\therefore \dfrac{{dR(x)}}{{dx}} = 126$
Hence, the marginal revenue at $x = 15$ is $126$.
So, the required solution is (d) $126$.

Note: To solve these types of problems, simply differentiate the given equation and substitute the value of the given variable to obtain an optimum solution.

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Concepts of Total Revenue, Average Revenue and Marginal Revenue  Forms of Market - Concepts of Total Average and Marginal Revenue  Revenue Formula  Average Revenue Formula  Prepaid Expenses, Accrued Income and Income Received in Advance  The Theory of Firm Under Perfect Competition and Revenue  Capital and Revenue Transactions  Capital and Revenue Items  Capital Receipt and Revenue Receipt  Capital Expenditures and Revenue Expenditures  