find the marginal revenue function.\nr(x)=x(15 - 0.02x)\nr(x)= square

Explanation:

Step1: Expand the revenue function

$R(x)=x(15 - 0.02x)=15x-0.02x^{2}$

Step2: Differentiate using power - rule

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $y = 15x$, $y^\prime=15$ (since $n = 1$ and $a = 15$), and for $y=-0.02x^{2}$, $y^\prime=-0.02\times2x=-0.04x$. $R^\prime(x)=\frac{d}{dx}(15x-0.02x^{2})=\frac{d}{dx}(15x)-\frac{d}{dx}(0.02x^{2}) = 15-0.04x$

Answer:

$15 - 0.04x$