A critical point in calculus is a point in the domain of a function where the function is either not differentiable or the derivative is equal to zero). More specifically, a point (x, f(x)) is called a critical point of f(x) if x is in the domain of the function and either f′(x) = 0 or f′(x) does not exist. Critical points are important in many application problems of the derivative, as they are places on the graph where the slope of the function is zero. All relative maxima and relative minima are critical points, but the reverse is not true. The value of the function at a critical point is a critical value). To find the critical point(s) of a function y = f(x), we need to find the derivative f (x) and then solve for the values of x where f (x) = 0 or f (x) is undefined.