Let us consider a function y=f{x} an open interval (a,b).For finding maxima or minima we find critical points where either

or the function is not continous.Suppose we find 4 critical points i.e. x_{1} ,x_{2 } ,a and b.

These critical point includes the end points.Now if we get local maxima from x_{1} and a & local minima from x_{2} and b.

Now absolute maxima and minima only exits if we get the ponts from x_{1} or x_{2} .

No absolute maxima and minimaexists if point is from open interval i.e. a or b.