Answered: 4) Determine the critical points of the…

4) Determine the critical points of the functions below and classify them as relative maximum, relative minimum or saddle point.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.CT: Test

Problem 11CT: aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _

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Question

4) Determine the critical points of the functions below and classify them as relative maximum, relative minimum or saddle point.

a) f(x,y) = x² - y² + 6xy
b) g(x,y)= 6x-x²-8y-2y²

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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