Hi I would just like for someone to check my proof/point out anything I am missing. Thanks!
Prove that the function is not diff at origin.
If it was differentiable at the origin, then should have the same derivative no matter how you approach the origin. We consider two paths approaching the origin from the x axis (positive side) and the line from the 1st quadrant.
Case 1 (x-axis):
Case 2 (x=y line):
Since these two limits are different. The function is not differentiable at the origin.