The Power of Zero

The most profitable move in calculus: set the derivative to zero and solve. That single trick finds peaks, valleys, and break-even points across every field.

Take online pricing. For each product, revenue = price × quantity sold. The derivative of revenue with respect to price equals zero at the revenue-maximizing price. Nudge the price up from there and you lose more customers than you gain per unit; nudge it down and the extra volume can't make up for the thinner margin.

Aircraft engineers use the same move to find the speed that wrings the most range out of every gallon of fuel.