Basic purpose of this article is to Analysis the Extreme Value Theorem. Here explain Extreme Value Theorem in mathematical point of view. A significant application of critical points is in determining possible highest and lowest values of a function on certain intervals. The Extreme Value Theorem assures both a maximum and minimum value for just a function under certain problems. The procedure for applying the Extreme Value Theorem is to first establish that your function is continuous about the closed interval. The next step is to determine all critical points inside given interval and measure the function at these critical points and with the endpoints of the period of time.