Let ū = (u1, u2) be a unit vector in R2 and let f: R2 → R be defined by if (x, y) # (0,0), f(x, y) = { x2 + y² if (x, y) = (0,0). (a) Find Dif(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?]

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