General purpose of this article is to Discuss on Critical Points in Calculus. This article explain Critical Points with theoretically and proper explanation in mathematical terms. Points for the graph of a function where the derivative is zero or the derivative isn’t going to exist are important to contemplate in many application problems of the derivative. The point ( x, f(x)) is called a vital point of f(x) if x was in the domain of the particular function and either f′(x) = 0 or f′(x) isn’t going to exist. The geometric interpretation of what’s taking place at a vital point is that the particular tangent line is possibly horizontal, vertical, or does not exist at that time on the curve.