Determine whether the statement "If f has a relative maximum at (x0, y0, z0), then fx(x0, y0) = fy(x0, y0) = 0" , is true or false. If it is false, explain why or give an example that shows it is false.

Determine whether the statement "If f has a relative maximum at (x0, y0, z0), then fx(x0, y0) = fy(x0, y0) = 0" , is true or false. If it is false, explain why or give an example that shows it is false.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Determine whether the statement "If f has a relative maximum at (x₀, y₀, z₀), then fx(x₀, y₀) = fy(x0_, y0) = 0" , is true or false. If it is false, explain why or give an example that shows it is false.

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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