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1. Let f(x, y) = 2x + xy^2 , x, y ∈ R. (a) Find the...

1. Let f(x, y) = 2x + xy^2 , x, y ∈ R.

(a) Find the directional derivative Duf of f at the point (1, 2) in the direction of the vector →v = 3→i + 4→j .

(b) Find the maximum directional derivative of f and a unit vector corresponding to the maximum directional derivative at the point (1, 2).

(c) Find the minimum directional derivative and a unit vector in the direction of maximal decrease at the point (1, 2).

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