Hi, I need help with this question:

3. Consider the function f : R8 -> R defined by f(x, y, 2) = x2 - ry3 -y?z+ 23 and the surface S of equation f(x, y, z) = 0. (a) Show that in a neighborhood of (1, 1, 1) the surface S is defined by an equation of the form z = $(r, y). Determine the tangent plane to S at (1, 1, 1). Compute the partial derivatives of order 2 of $ near (1, 1). What is the position of the surface S with respect to its tangent plane at (1, 1, 1)