Maxima and Minima in Calculus

In calculus, maxima and minima are points on a curve where a function reaches its highest or lowest value locally or globally. A maximum occurs where the function peaks—think of the top of a hill—so the function value is higher than nearby points. Conversely, a minimum is where the function dips—like the bottom of a valley—being lower than neighboring values. These points are critical for understanding the behavior of functions, optimizing problems, or analyzing trends. Mathematically, maxima and minima occur where the derivative (rate of change) is zero or undefined, indicating a potential shift in the function’s increasing or decreasing pattern.