Let f(x,y) = $\displaystyle \frac{x^{2}(x - y)}{x^{2} + y{2}}$ if (x,y) doesnt equal (0,0) and

0 if x = y = 0

a) Find $\displaystyle f_x$(0,0) and $\displaystyle f_y$(0,0)

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

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

Attempt:

a) $\displaystyle F_x$(0,0) and $\displaystyle f_y$(0,0) both = 0

b) No since f(x,y) = 0 (if x = y = 0) and $\displaystyle \frac{x^{2}(x - y)}{x^{2} + y{2}}$ (if (x,y) doesnt equal (0,0)

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