Critical Value in Calculus. In calculus, critical values are the points at which a function has the maxima or minima. For finding the critical values of a function f(x), we first find f'(x), then solve f'(x) = 0, suppose we get x = c 1, c 2, c 3, ........ Then, c 1, c 2, c 3, .....are the critical points, at which f(x) can have maxima or minima.