Answered: Find the critical points of f(x, y) =…

Find the critical points of f(x, y) = x^3-y^3+xy and classify each point as a relative maximum, a relative minimum, or a saddle point.

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

Section9.3: Maxima And Minima

Problem 2YT

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Question

Find the critical points of f(x, y) = x^3-y^3+xy
and classify each point as a relative
maximum, a relative minimum, or a saddle point.

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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