If f is differentiable at c and f′(c) = 0, then we call c a critical point or stationary point of f. A point c at which the derivative of f is not defined is called a singular point of f.
Thus we know that the candidates for the location of the extreme values of a continuous function on a closed interval fall into three categories: (a) endpoints of the interval, (b) critical points, and (c) singular points. To determine the extreme values of such a function f, we identify all these points, evaluate f at each one, and identify the largest and smallest values.
