Final answer:
To identify the stationary point of the function f(x,y), calculate the partial derivatives, set them to zero, and solve the equations. Then use the second derivative test to determine the nature of the stationary point by evaluating the Hessian determinant.
Step-by-step explanation:
The question is asking to find the stationary point of a function f(x,y) and determine whether it is a maximum, minimum, or saddle point. To find the stationary points, we need to calculate the partial derivatives of the function with respect to x and y, and set them equal to zero. Then we solve the system of equations to find the coordinates of the stationary point.
After locating the stationary point, we employ the second derivative test for functions of two variables. This involves computing the second partial derivatives and evaluating the Hessian determinant at the stationary point. A positive value indicates a minimum, a negative value indicates a maximum, and if it equals zero, it may be a saddle point. The specific criteria are based on the signs of the second partial derivatives and the determinant of the Hessian matrix.