1. Let z = f(x,y) be implicitly defined by xz = √(3x2 + y - z2). Find the equation of the tangent plane and the equation of the normal line to the surface z = f(x,y) at P = (1, 1, √2). Justify your procedure and Simplify.
2. Find the unit vector in the direction of greatest rate change of f at P and the dire, derivative of f in that direction.