3. Consider the function f (x, y) = 2mg 2:2 2y2 + 4.93. 3f 3f (a) Determine the rst order partial derivatives and 8:1: 6y' 32f 32f 32 f (b) Determine the second order partial derivatives 5, 8:): (931' and 5112. (0) Find the equation of the tangent plane at the point (1,1,3) to the surface z = f (x, y). (d) Find the linearization L(a:, y) of f (as, y) at the point P0(1,1). (e) Find the direction u in which f increases most rapidly at P0( 1, 1) and then nd the derivative of f in this direction. (f) Determine the critical p0int(s) of f. (g) Find the local extrema of f