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# The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue).If the total revenue(in rupees) received from the sale of Xunits of a product is given by R(x)=$3x^2+36x+5$,find the marginal revenue,when x=5,and write which value does the question indicate.

This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.

Toolbox:
• If the Total Revenue is given by $f(x)$, the Marginal Revenue is the rate of change of total revenue and is nothing but the first order derivative of the function $\large \frac{df(x)}{dx}$
Given the total revenue $=R(x)=3x^2+36x+5$.
If the Total Revenue is given by $f(x)$, the Marginal Revenue is the rate of change of total revenue and is nothing but the first order derivative of the function $\large \frac{df(x)}{dx}$
$\Rightarrow$ Differentiating $R(x)$, we get $\large \frac{dR(x)}{dx}$$= 6x+36$
If $x=5$, Marginal revenue $= 6 (5) + 36$
Therefore, Marginal revenue $= 30+36 = 66$.
The concern over the welfare of the employees by the employer.

edited Mar 22, 2013