"find and classify the extreme point $\displaystyle (x,y)$ of the function of two variables $\displaystyle f(x,y) = x^2 + y^2 - xy$" States the question

My solution:

dz/dx = 2x - y

dz/dy = 2y - x

y = x = 0

therefore the extrema point is at (0,0)

to classify it:

$\displaystyle D = \frac{d^2z}{dx^2} . \frac{d^2z}{dy^2} - \frac{d^2z}{dxdy}

$

$\displaystyle D = 2 . 2 - (-1)^2 = 3$

3 > 0 which means the extrema is a local minima

Am I correct?

Thank you