The critical points of a function are the points where the function changes direction. If the function was increasing and reaches a critical point, it starts decreasing there. Conversely, if a function was decreasing and reaches a critical point, then it starts increasing there. Therefore, the critical points of a function are the points that represent local maxima and minima of the function (its extrema). To find critical points, Take the derivative of the function and set the derivative equal to 0 Find the values of x that make the derivative equal to 0, or make it undefined. These are the critical numbers. Use the first derivative test to see whether or not the function actually changes direction at the critical numbers. Verify that the critical numbers are in the domain of the function. If a critical number is in the domain of the function and the first derivative test tells you that the function changes direction at the critical number, then the critical number is in fact a critical point of the function, and it therefore represents at least a local maxima or local minima of the function. Depending on the function's value everywhere else, the critical point may also be the function's absolute maximum or absolute minimum.