Find the local max, min, and saddle point for the function:
f(x,y) = 2x^2+3xy+4y^2-5x+2y
The Attempt at a Solution
I've taken the two partial derivatives
Fx = 4x + 3y - 5
Fy = 3x + 8y + 2
I know that the critical points will sit where both of theses partial derivatives = 0
Fx = 4x + 3y - 5 = 0
Fy = 3x + 8y + 2 = 0
The problem I have here though is that I don't know how to solve the system of equations.
I know once I've solved the system of equations I can use the determinant of the jacobian matrix to see whether they are local max, min, or saddle points...
Any help with solving the system of equations would be much appreciated. I've had a bit of trouble solving systems of equations in the past.