I need the answer and steps to understand how :) Example 0.5.1. Given the function g(x, y, z) = x² + 2y² + 3z². Find a unit vector ū such that therate of increase of g(x, y, z) at the point (1,2,3) in direction of u is maximum. Evaluate the greatestrate of increase of g in the direction of u.

Answered: Image /qna-images/answer/82f57235-547f-47ca-b6bf-d9baa354443e.jpg

Example 0.5.1. Given the function g(x, y, z) = x² + 2y² + 3z². Find a unit vector u such that the rate of increase of g(x, y, z) at the point (1,2,3) in direction of u is maximum . Evaluate the greatest rate of increase of g in the direction of u.

Example 0.5.1. Given the function g(x, y, z) = x² + 2y² + 3z². Find a unit vector u such that the rate of increase of g(x, y, z) at the point (1,2,3) in direction of u is maximum . Evaluate the greatest rate of increase of g in the direction of u.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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I need the answer and steps to understand how :)

Example 0.5.1. Given the function g(x, y, z) = x² + 2y² + 3z². Find a unit vector ū such that the
rate of increase of g(x, y, z) at the point (1,2,3) in direction of u is maximum. Evaluate the greatest
rate of increase of g in the direction of u.

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