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The value of the directional derivative of the function θ (x, y, z) = xy2 + yz2 + zx2 at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is
  • a)
    1
  • b)
    0.95
  • c)
    0.93
  • d)
    0.9
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The value of the directional derivative of the function θ (x, y,...
Given that,
ϕ = xy2 + yz2 + zx2
directional vector (p) = I + 2j + 2K
Directional derivative = 
∇ϕ at the point (2, -1, 1) is
∇ϕ = ((-1)2 + 2(2)(1)) î + (2(2)(-1) + (1)2) ĵ + (2(-1)(1) + (2)2)k̂
= 5î - 3ĵ + 2k̂
Directional derivative = 
= 5 - 6 + 4 / 3
= 1
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The value of the directional derivative of the function θ (x, y, z) = xy2+ yz2+ zx2at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k isa)1b)0.95c)0.93d)0.9Correct answer is option 'A'. Can you explain this answer?
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