Let a be a real number and f(x, y) = 4ax?y+ 3xy³. 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. -16/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is find a.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let a be a real number and f(x, y) = 4ax?y+ 3xy³.
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.
- 16/5
ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is
V2
find a.
Transcribed Image Text:Let a be a real number and f(x, y) = 4ax?y+ 3xy³. 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. - 16/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a.
О0 (8а + 3) і + (4а + 9) j, i) -4
O i) (8a + 3) i + (4a + 9) j, ii) -12
O i) (8a + 3) i + (4a + 9) j, ii) 12
O i) (8a + 3) i + (4a + 9) j, ii) 0
O i) (4a + 3) i + (-8a + 9) j, ii) -4
о) (4а + 3) і + (-8а + 9) ј, i) -12
O i) (4a + 3) i + (-8a + 9) j, ii) 12
O i) (4a + 3) i + (-8a + 9) j, ii) 0
Transcribed Image Text:О0 (8а + 3) і + (4а + 9) j, i) -4 O i) (8a + 3) i + (4a + 9) j, ii) -12 O i) (8a + 3) i + (4a + 9) j, ii) 12 O i) (8a + 3) i + (4a + 9) j, ii) 0 O i) (4a + 3) i + (-8a + 9) j, ii) -4 о) (4а + 3) і + (-8а + 9) ј, i) -12 O i) (4a + 3) i + (-8a + 9) j, ii) 12 O i) (4a + 3) i + (-8a + 9) j, ii) 0
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