A firm's profit, in thousands of rupees, from selling $x$ units is $P(x) = -x^2 + 60x - 500$. What is the largest profit?

Explanation

1. 01

   $P'(x) = -2x + 60 = 0$ at $x = 30$; $P'' = -2 < 0$, a maximum.

2. 02

   $P(30) = -900 + 1800 - 500 = 400$ thousand rupees.