Explanation Consider the given statement: A function of two variables may have both a relative maximum and an absolute maximum at the same point. The given statement is true. A relative maximum or relative minimum at a point ( a , b ) means that in the immediately vicinity of that point, f ( x , y ) has maximum or minimum value at that particular point, that is, f ( a , b ) > f ( a ± h , b ± h ) Now, if h extends to ∞

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.CR, Problem 8CR

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The given statement is true or not and give the reason.

Statement: “A function of two variables may have both a relative maximum and an absolute maximum at the same point”.

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Chapter 9.CR, Problem 7CR

Chapter 9.CR, Problem 9CR

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

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The given statement is true or not and give the reason. Statement: “A function of two variables may have both a relative maximum and an absolute maximum at the same point”.

Solution Summary: The author evaluates whether the given statement is true or not, and explains that a function of two variables may have both relative maximum and absolute maximum at the same point.