Theorem of the Maximum

The Theorem of the Maximum states that for certain types of functions, if you look at all the possible input values, the highest point (or maximum) occurs where the first derivative (rate of change) is zero, and the second derivative confirms it's a maximum (usually negative). In simpler terms, it helps identify the peak of a curve by finding where the slope flattens out, indicating a turning point. This is useful in optimization problems to find the best possible value, such as maximum profit or efficiency.