Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f (x, y) at the critical point (x0, y0). fxx(x0, y0) = −3, fyy(x0, y0) = −8, fxy(x0, y0) = 2

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f (x, y) at the critical point (x0, y0). fxx(x0, y0) = −3, fyy(x0, y0) = −8, fxy(x0, y0) = 2

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 7CR

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Question

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function f (x, y) at the critical point (x₀, y₀). fxx(x₀, y₀) = −3, fyy(x₀, y₀) = −8, fxy(x₀, y₀) = 2

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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