4. For the surface x2 In(z) +y z = x, a) Define F such that F(x, y, z) = 0. Assume z = f(x, y) and find Vf at the point (1, -1, 1). Hint: The gradient is a vector in 2D, Vf =, where fx and fy can be found implicitly. b) Find the rate of change of the surface at the point (1, -1, 1) in the direction u = -31 + 4j. That is, find Duf(1, -1, 1).Reference: The problems are based on the third weeks' lectures and Thomas' Calculus. Early Transcendentals, 14th ed., sections 14.5-14.7