Let a be a real number and f(, y) = 5aa?y + 5æy³. Let v = 3i – j and let Vf(r, y) denote the gradient of f(x, y). i) Find Vf(1,1) in terms of a. -10/5 , find a. ii) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is - v2 O ) (10a + 5) i + (5a + 15) j, i) -2 O i) (10a + 5) i + (5a + 15) j, ii) -6 O i) (10a + 5) i + (5a + 15) j, i) 6 O i) (10a + 5) i + (5a + 15) j, ii) 0 O i) (5a + 5) i + (-10a + 15) j, ii) -2 i) (5a + 5) i + (-10a + 15) j. ii) -6 O i) (5a + 5) i + (-10a + 15) j. ii) 6 i) (5a + 5) i + (-10a + 15) j, i) 0

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Let a be a real number and f(x, y) = 5aa?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.
-10/5
i) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is
v2
find a.
O i) (10a + 5) i + (5a + 15) j, ii) -2
O i) (10a + 5) i + (5a + 15) j, i) -6
O i) (10a + 5) i + (5a + 15) j, i) 6
O i) (10a + 5) i + (5a + 15) j, i) 0
O i) (5a + 5) i + (-10a + 15) j, i) -2
i) (5a + 5) i + (-10a + 15) j, i) -6
i) (5a + 5) i + (-10a + 15) j, i) 6
O i) (5a + 5) i + (-10a + 15) j, i) 0
Transcribed Image Text:Let a be a real number and f(x, y) = 5aa?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. -10/5 i) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is v2 find a. O i) (10a + 5) i + (5a + 15) j, ii) -2 O i) (10a + 5) i + (5a + 15) j, i) -6 O i) (10a + 5) i + (5a + 15) j, i) 6 O i) (10a + 5) i + (5a + 15) j, i) 0 O i) (5a + 5) i + (-10a + 15) j, i) -2 i) (5a + 5) i + (-10a + 15) j, i) -6 i) (5a + 5) i + (-10a + 15) j, i) 6 O i) (5a + 5) i + (-10a + 15) j, i) 0
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