Finding Local Max and Min values and saddle in mult. Calculu

[Physicsnoob90]

Homework Statement

Find the local maximum and minimum values and saddle points of the function
f(x,y) = x^2 + xy + y^2 + y

Homework Equations

Local max/min
critical points
saddle

The Attempt at a Solution

1) partial derivative: fx = 2x+y fy = x+2y+1

from here, I'm a little confuse on what should i do to find the critical point in order to solve for the local max/min.

 

[LCKurtz]

Homework Statement

Find the local maximum and minimum values and saddle points of the function
f(x,y) = x^2 + xy + y^2 + y

Homework Equations

Local max/min
critical points
saddle

The Attempt at a Solution

1) partial derivative: fx = 2x+y fy = x+2y+1

from here, I'm a little confuse on what should i do to find the critical point in order to solve for the local max/min.

Set the two partials equal to zero and solve for the critical point $(a,b)$. Then test it.