Identifying Stationary Points (Critical Points) for a Function

Identifying stationary points, also known as critical points, is a fundamental concept in calculus and optimization, essential for understanding the behavior of functions and locating extrema. Stationary points occur where the derivative of a function equals zero or is undefined, indicating potential peaks, troughs, or points of inflection. Through rigorous analysis of these critical points, mathematicians and scientists can elucidate the local behavior of functions, optimize processes, and solve a wide array of practical problems in fields ranging from physics and engineering to economics and biology.