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The maximum value of the directional derivative of the function ϕ = 2x2 + 3y2 + 5z2 at point (1, 1, -1) is

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  1. 5
  2. 152
  4. -10

Answer (Detailed Solution Below)

Option 3 :

Detailed Solution

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Concept:

Gradient:

For a scalar function ϕ(x, y, z), the gradient is the maximum rate of change which is given by-

Directional derivative:

It gives the rate of change of scalar point function in a particular direction. The maximum magnitude of the directional derivative is the magnitude of the gradient.

Calculation:

Given:

ϕ = 2x2 + 3y2 + 5z2

∇ϕ = 4xî + 6yĵ + 10zk̂

∇ϕ(1, 1, -1) = 4î + 6ŷ - 10k̂

Maximum value is given by the magnitude,

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