Question

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

Answer 1

As given, marginal revenue is the rate of change total revenue with respect to the number of items sold at an instant.
Let $M.R.$ be marginal revenue, so

$M.R.=\frac{dR}{dx}$

It is given $R\left(x\right)=3x^2+36x+5$

$M.R.=\frac{d}{dx}(3x^2+36x+5)$

$\Rightarrow M.R.=6x+36$

When $x=5$, we get

$\Rightarrow M.R.=30+36=66$

Hence, the required marginal revenue is Rs. $66$.