Let S be the system of equations x-u-v=0, y-u^2-v^2=0 and z-u^3-v^3=0. Find point P=\{x_0,y_0,z_0,u_0,v_0\} such that:

a) Around P, the system S implicitly defines three differentiable functions: z=f_1(x,y),\, u=f_2(x,y),\,v=f_3(x,y).

b) The directional derivative of f_1 in (x_0,y_0) is maximum according the direction of the vector (0,1) and the value of the aforesaid directional derivative is 3.


I don't get very well what to do in part a), as for b), how can I compute the directional derivative?