Critical Points

Critical points are specific values of a function where its behavior changes, such as reaching a highest or lowest point. Mathematically, these are points where the derivative (rate of change) of the function is zero or undefined. In simple terms, they help identify potential peaks (maxima), valleys (minima), or flat spots on a graph. Critical points are important in optimization and analyzing how a function behaves, as they mark where the function might switch from increasing to decreasing or vice versa, providing insight into the function’s overall shape and key features.