Answered: True or False: Given a function of two…

True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular to the graph z = f(x, y) at the point with (x, y) = (a, b). O True O False

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 13CR

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Question

True or False: Given a function of two variables f(x, y), the vector Vf(a, b) is perpendicular
to the graph z = f(x, y) at the point with (x, y) = (a, b).
True
False

Expert Solution

Solution:

It is false.

The gradient vector $\nabla f (a, b)$ is not perpendicular to the graph $z = f (x, y)$ at the point with $(x, y) = (a, b)$ .

The gradient vector $\nabla f (a, b)$ is perpendicular to the level curve on the graph $z = f (x, y)$ at the point with $(x, y) = (a, b)$ .

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