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

A:

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A:

Q: 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) =…

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A: To find  is the unit vector parallel to .

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Q: Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and…

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