z=f(x,y)=(y-x^2)(y-2x^2)

a) Show that the point (0,0) is a critical point of f ' and that the second derivative test for a function of two variables fails at this critical point

b) Show that f has neither a maximum nor a minimum at (0,0) by proving that there are values of the parameter a for which f has a maximum at (0,0) along the parabolas y=ax^2, while for other values of parameter a, the function f has a minimum at (0,0) along the parabolas y=ax^2.

c) Show that f has a minimum at (0,0) along every straight line through(0,0)

This is really urgent to me, i need this for my test

Can anyone show me how to do? Thanks very much!