Answered: Suppose f(x,y)=xy(1−1x−10y) f(x,y)…

Suppose f(x,y)=xy(1−1x−10y) f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.2: Polynomial Functions

Problem 96E: What is the purpose of the Intermediate Value Theorem?

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Question

Suppose f(x,y)=xy(1−1x−10y)
f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point.

First point ( ,  ) of type ___
Second point ( ,  ) of type ______-
Third point ( ,  ) of type ________-
Fourth point ( ,  ) of type ________

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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