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Classify all critical points of the function f(x,y)=x^2-y^2+4x-2y+1.

I know I have to take the partial derivative and set them equal to zero to get my points and then use the Hessian. For some reason I am not getting the correct answer.
partial d/dx 2x+4 and partial d/dy 2y-2 and solving each for zero gives me x=-2 and y=1

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