Let a be a real number and f(x, y) = 4ax?y + 5xy³. Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y). i) Find Vf(1, 1) in terms of a. -12/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a.

Q: Compute the gradient of the function at the given point. f(x, y) = 10x - 8y, (10,8)

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Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

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Q: Let a be a real number and f(r, y) = 4az?y+ 8zy". Let v = 3i – j and let Vf(x, y) denote the…

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Q: Let a be a real number and f(x, y) = 4ax?y + 8ry³. Let v = 3i – j and let Vf(r, y) denote the…

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Q: Let a be a real number and f(, y) = 5aa?y + 5æy³. Let v = 3i – j and let Vf(r, y) denote the…

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