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Find critical points for

f(x,y)= x^3+y^3-15x^2-6xy+18y^2+39x+138y

I know you first take the partial derivative of x and y, but I am not sure where to go from there.

1 answer

critical points are where they are both zero. So, you need

x^3+y^3-15x^2-6xy+18y^2+39x+138y
3x^2-30x-6y+39 = 0
3y^2-6x+36y+138 = 0

http://www.wolframalpha.com/input/?i=solve+3x%5E2-30x-6y%2B39+%3D+0,+3y%5E2-6x%2B36y%2B138+%3D+0

http://www.wolframalpha.com/input/?i=minima+x%5E3%2By%5E3-15x%5E2-6xy%2B18y%5E2%2B39x%2B138y
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