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Problem 13 - Entrance Test

Find the directional derivative of f(x, y) = x^2y + y^3 at the point (1, 2) in the direction of the vector v = <3, 4>.

Correct: C

∇f = <2xy, x^2 + 3y^2>. At (1, 2), ∇f(1, 2) = <4, 13>. Unit vector in the direction of v: u = <3/5, 4/5>. Du f(1, 2) = ∇f(1, 2) · u = <4, 13> · <3/5, 4/5> = (12/5) + (52/5) = 64/5.