The total revenue in Rupees received from the sale of x units of a product is given by $R (x) = 3 x^{2} + 36 x + 5$ . Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant

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Detailed Solution

Since marginal revenue is the rate of change of total revenue with respect to
the number of units sold, we have
Marginal Revenue $(MR) = \frac{dR}{dx} = 6 x + 36$
When x = 5, MR = 6(5) + 36 = 66
Hence, the required marginal revenue is Rs. 66

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