Question

ple - 11 : In what direction from (3, 1, -2) is the directional derivative of u = x+y_74 maximum? Find the magnitude of the maximum.​

Answer 1

Answer:

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Explanation:

The directional derivative in the direction of the unit vector d^ is

∇F⋅d^=|∇F||d^|cos(θ)

Since |d^|=1 and the maximum value of cos(θ)=1 (achieved when θ=0 and d^ points in the same direction as the gradient) the maximum directional derivative is in the direction of ∇F and has value |∇F|. Only the gradient of F is required, a^ does not come in to it.