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**toop** Let *S* be the set of all points inside of the triangle whose vertices are

$\displaystyle (-2,0), (0,2), (2,0).$

Find the minimum and maximum values of the function

$\displaystyle f(x,y) = x^2 + 3y^2 - 4xy + x - y +1$

The equations for the sides of this triangle are:

$\displaystyle y=0 , -2 \leq x \leq 2$

$\displaystyle y = 2-x , 0 \leq x \leq 2$

$\displaystyle y = 2+x , -2 \leq x \leq 0$

From what I comprehended in class and in my notes, I substitute $\displaystyle y$ into the original function and then take the derivative of the result. I then set the derivative equal to 0 to find the critical points?

From there I am not too sure what to do...I assume I do it for all three equations and then plug it back into the original function to find the min/max?