7. Suppose that f is the scalar field that turns each point (x1, X2, X3, ... , x100) in R100 into the sum of its coordinates. a) What can we say about Vƒ(x1,x2, X3, ... , X100)? b) Does f have any critical points? If so, what are they? If not, why not?
7. Suppose that f is the scalar field that turns each point (x1, X2, X3, ... , x100) in R100 into the sum of its coordinates. a) What can we say about Vƒ(x1,x2, X3, ... , X100)? b) Does f have any critical points? If so, what are they? If not, why not?
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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Transcribed Image Text:7. Suppose that \( f \) is the scalar field that turns each point \( (x_1, x_2, x_3, \ldots, x_{100}) \) in \( \mathbb{R}^{100} \) into the sum of its coordinates.
a) What can we say about \( \nabla f(x_1, x_2, x_3, \ldots, x_{100}) \)?
b) Does \( f \) have any critical points? If so, what are they? If not, why not?
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