Let a be a real number and f(r, y) = 4ar?²y+ 8zy. Let v = 3i – j and let Vf(z, y) denote the gradient of f(z, y). i) Find Vf(1, 1) in terms of a. -125 i) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is V2 find a. O i) (8a + 8) i + (4a + 24) j, ii) -3 O ) (8a + 8) i + (4a + 24) j, i) -9 O ) (8a 8) i + (4a + 24) j, i) 9 + 8) i + (4a + 24) j, i) O O ) (4a + 8) i + (-8a - 24) j, i) -3 O ) (4a + 8) i + (-8a - 24) j, i) -9 + 8) i + (-8a + 24) j, ii) 9 O ) (8a O ) (4a O ) (4a + 8) i + (-8a - 24) j, i) O

Q: (a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change…

A: The given function f(x,y,z)=xy+yz2+xz3, P(2,0,3)u=-23,-13,23

Q: Consider the following. f(x, y) = ₁ P(9, 1), u = ¹+1 (a) Find the gradient of f. Of(x, y) = (b)…

A: The gradient of f(x, y) is calculated using the formula: ∇f=∂f∂xi+∂f∂yj.

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A: From the basic vector calculus

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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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