Thread: Determining the type of critical point when the second derivative test fails

For example with
Well I know there is a critical point at (0,0). So I calculated the second derivatives but they are all 0 here so that doesn't help.
I also tried using the Taylor expansion to show that f(x,y)>f(0,0) or not but that didn't get me anywhere.
Then I tried considering the type of critical point on x=0,y=0,y=-x etc. but again I didn't get anywhere.
Any ideas?

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If y=x

if x<0 f(x,y)<0
if x>0 f(x,y)>0.
(0,0) is not min point.