says

## Homework Statement

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
i.e.

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.

Staff Emeritus
Homework Helper

## Homework Statement

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
i.e.

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.

Really? You never solved a set of simultaneous linear equations in your algebra courses?

You can use Cramer's Rule or elimination to solve the system above.

http://www.coolmath.com/algebra/14-determinants-cramers-rule/01-determinants-cramers-rule-2x2-01

http://www.purplemath.com/modules/systlin6.htm

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.