Using the second order derivative we find out whether a given stationary point of a function is a local maximum or a local minimum. Let f(x) be any function describing the nature of a real life system (movement of gas molecules, motion of a body on a curve, life time of a fuels etc) Then as per the second order derivatve test if:
1. f''(x) >0, the function f(x) has a minimum at x.
2. f''(x) <0, the function has a maximum at x.
3. f''(x) = 0, it is not able to predict the nature of the curve at point x.