Chapter 4.5, Problem 36E

Total Revenue Suppose that the total revenue function for a manufacturer is $R(x)=300\ln (x+1)$, so the sale of $x$ units of a product brings in about $R(x)$ dollars. Suppose also that the total cost of producing $x$ units is $C(x)$ dollars, where $C(x)=2x$. Find the value of $x$ at which the profit function $R(x)=C(x)$ will be maximized. Show that the profit function has a relative maximum and not a relative minimum point at this value of $x$.