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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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 ∇fa,b is not perpendicular to the graph z=fx, y at the point with x, y=a,b.

The gradient vector ∇fa,b is perpendicular to the level curve on the graph z=fx, y at the point with x, y=a,b.

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