Question

8. Find a unit vector in the direction in which $f(x, y, z) = \csc^{-1}(\frac{yx}{3x-3z})$ increases most rapidly at P(4,2,1), and find the rate of change of $f$ at P in that direction.

Name: 8. Find a unit vector in the direction in which f(x, y, z) = csc^-1((yx)/(3x-3z)) increases most rapidly at P(4,2,1), and find the rate of change of f at P in that direction.
Uploaded: 2022-03-24T11:58:22-08:00
Duration: 3 min 15 s
Channel: Vincenzo Zaccaro
Description: 8. Find a unit vector in the direction in which f(x, y, z) = csc^-1((yx)/(3x-3z)) increases most rapidly at P(4,2,1), and find the rate of change of f at P in that direction.

          8. Find a unit vector in the direction in which $f(x, y, z) = \csc^{-1}(\frac{yx}{3x-3z})$ increases most rapidly at P(4,2,1), and find the rate of change of $f$ at P in that direction.

8. Find a unit vector in the direction in which f(x, y, z) = csc^-1((yx)/(3x-3z)) increases most rapidly at P(4,2,1), and find the rate of change of f at P in that direction.

Added by Aitor B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

03/24/2022

Step 1

The gradient of a function is a vector that points in the direction of the greatest rate of increase of the function. It is calculated by taking the partial derivatives of the function with respect to each variable. Given f(x,y,z) = csc^(-1)(3x-3z), the gradient Show more…

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please solve it step by step yx 8. Find a unit vector in the direction in which f(x,y,z) = csc-1 3x-3z increases most rapidly at P(4,2,1), and find the rate of change of f at P in that direction.