Second derivative test.ipynb

Kernel: SageMath (stable)

%display latex # make math display nice

var("x y") # make x and y symbols
f = (2*x^2 + 3*y^2)*exp(-x^2-y^2) # define f
D = diff(f,x,2)*diff(f,y,2) - diff(f,x,y)^2 # define D for the second derivative test

D2 = expand(D*e^(2*x^2+2*y^2)) # simplify D and clear out the exponential factor
D2

# inspect values at critical points
[D2(x=a,y=b) for (a,b) in ((0,0),(1,0),(-1,0),(0,1),(0,-1))]