3. Consider the function f(x, y) = x2 + xy ty - x+y. af of (a) Determine the first order partial derivatives and ax ay 22 f (b) Determine the second order partial derivatives and ax2' ardy ay2 (c) Write the equation of the tangent line at the point (x, y) = (-2,3) to the surface z = f(x, y). (d) Find the linearization L(x, y) of f(x, y) at the point Po(-2, 3). (e) Find the direction (u) in which f increases most rapidly at Po(-2, 3) and find the derivative of f in this direction. (f) Determine the critical point(s) of f. (g) Find the local extrema of f specifying their nature