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The magnitude of the directional derivative of the function f(x, y) = x2 + 3y2 in a direction normal to the circle x2 + y2 = 2, at the point (1, 1), is
  • a)
    4√2
  • b)
    5√2
  • c)
    7√2
  • d)
    9√2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The magnitude of the directional derivative of the function f(x, y) = ...
F(x,y) = x2 + 3y2
ϕ = x+ y2 – 2
point P (1, 1)
Normal to circle x2 + y2 - 2 is
∇ϕ = 2xi + 2yj
At P (1, 1)
Normal Vector, a = 2i + 2j
Magnitude of directional derivative of f along normal vector is ∇f. a
= 2xi + 6yj
At P(1,1)
∇ f = 2i + 6j
Directional derivative, = ∇f . a
= 4√2
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