Let f(x,y) = if (x,y) doesnt equal (0,0) and

0 if x = y = 0

a) Find (0,0) and (0,0)

b) Is f continuous at (0,0)?

c) Is f differentiable at (0,0)? Explain.

Attempt:

a) (0,0) and (0,0) both = 0

b) No since f(x,y) = 0 (if x = y = 0) and (if (x,y) doesnt equal (0,0)

c) It isnt differentiable at (0,0) similar reasoning as b