If the total revenue received from the sale of $x$ units of a product is, $R (x) = 5 x^{3} + 4 x^{2} + 8 x + 12$ , then the marginal instantaneous revenue when $x = 4$ is _____

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Solution

Marginal revenue is assumed as the rate of change of sale revenue at any level of output.

Given, $R (x) = 5 x^{3} + 4 x^{2} + 8 x + 12$
Marginal revenue, $M R = \frac{d}{d x} R (x) = 15 x^{2} + 8 x + 8$
At $x = 4, M R = 15 (4^{2}) + 8 (4) + 8 = 280$

Hence, required marginal revenue is $R s . 280$ .

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