I have the function f(x,y)= 2x^3 + 3xy + 2y^3, I have found the 2 critical points for x in R and y in R.

I believe they are (0,0) and (-1/8, 1/2)?!

I then found that they are both saddle points which is when I doubted whether these critical points are correct.

I then have to sketch the contours which I have attempted but am unsure if I have constructed the sketch correctly.