Sometimes first derivatives fail to determine the maxima and minima of the function.
So, the second derivative test is done to determine the maxima and minima of the function.
The function is maximum at the point where the first derivative of the function is equal to zero and the second derivative is negative. That is at , then has local maxima at .
The function is minimum at the point where the first derivative of the function is equal to zero and the second derivative is positive. That is at , then has local minima at .
To find the saddle point, we use partial second-order derivatives.