The cost and the revenue functions of a profit maximizing firm are \(C=Q^3-59Q^2+1315Q+2000\) and…

The profit-maximizing output is 35 units. Profit is $\pi$ $=R-C$ $=-Q^3+57Q^2-315Q-2000$, so $d\pi/dQ$ $=-3Q^2+114Q-315$ $=-3(Q-3)(Q-35)$. The stationary outputs are 3 and 35, and $d^2\pi/dQ^2=-6Q+114$ is negative at 35 and positive at 3. Profit at 35 is 13,925, exceeding profit of -2,000 at zero output.