The money to be spend 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 `x` units of a product is given by `R(x)=3x^2+36 x+5,` find the marginal revenue, when `x=5,` and write which value does the question indicate.

Explanation

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 `frac{d f(x)}{d x}`


Total revenue `=R(x)=3 x^{2}+36 x+5`


Differentiating the equation `R(x)`, we get



`frac{d(x)}{d x}=6 x+36`



If `x=5`, Marginal revenue `=6(5)+36=66`.


Therefore, the Marginal revenue `=66`.


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