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15 votes
15 votes
Find the direction in which the function is increasing most rapidly at the point Po.

f(x, y,z)= xy -lnz , Po (1,1,1)

User Myke
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1 Answer

26 votes
26 votes

The largest rate of change occurs in the same direction as the gradient of f at the point.

f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y, x, -1/z)

==> ∇f (1, 1, 1) = (1, 1, -1)

In other words, f changes at the highest rate in the direction of the vector (1, 1, -1).

User Emrass
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