Chapter 4.1, Problem 63E

Total revenue from marginal revenue. Eloy Chutes determines that the marginal revenue, $R^{\prime }$, in dollars per unit, from selling the $x\text{th}$

parachute is given by

$R^{\prime }\left(x\right)=x^2-3$

$R\left(x\right)=\frac{x^3}{3}-3x$

a. Find the total-revenue function, R, assuming that $R\left(0\right)=0$

b. Why is $R\left(0\right)=0$ a reasonable assumption?