I have solved part(a) and (b), but I have no ideas on part (c).

Q4. Let u = (u1, u2) be a unit vector in R2 and let f : R2 -> R be defined by x 2 y f (x, y) = 2 0 2 + y 2 if ( x, y) * (0,0), O if ( x, y) = (0, 0). (a) Find Duf (0, 0). (b) Using your solution to (a), find Vf(0, 0). (c) Use the Lagrange multipliers algorithm to find the maximum and minimum directional derivatives at (0, 0). Hint: What are you trying to optimize? What is the constraint?]