1. ## Marginal Revenue problem

The revenue $R$ (in dollars) from renting $x$ apartments can be modeled by:

$R=2x(900+32x-x^2)$

Find the additional revenue when the number of rentals is increased from 14 to 15, and find the marginal revenue when x=14.

How can I differentiate this problem and solve it down?

2. Hi hemi,

We have;

$\mbox{R}(x)=2x(900+32x-x^2)=1800x+64x^2-2x^3$

so

$\mbox{R}(14)=1800(14)+64(14)^2-2(14)^3$

$\mbox{R}(15)=1800(15)+64(15)^2-2(15)^3$

It's worthwile noting that $\frac{d}{dx}(x^n)=nx^{n+1}$ , so

$\mbox{MR}=\mbox{R}'(x)=1800+128x-6x^2$

Can you finish?