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?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 22E: Prove that if R and S are fields, then the direct sum RS is not a field. [Type here][Type here]

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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 (xX1, X2, X3, ... , X10o)?
b) Does f have any critical points? If so, what are they? If not, why not?

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