Many marginal cost curves are U-shaped. As a result, it is possible that the MC curve hits the demand or price line at two output levels. Which is the profit-maximizing output? Why

Many marginal cost curves are U-shaped., because the marginal cost i s relatively high at small quantities of output and is not proportional with the production increases.

Profit is maximized when marginal cost curve intersects demand from below because at any greater quantity than this marginal cost is greater than marginal revenue.