Answered: f (x,y) = 2x^3 + y^2 - 9x^2 - 4y + 12x…

f (x,y) = 2x^3 + y^2 - 9x^2 - 4y + 12x +1028. Find all critical points of f. For each critical point, determine whether it is a relative maximum, a relative minimum, or a saddle point of f

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?

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Question

f (x,y) = 2x^3 + y^2 - 9x^2 - 4y + 12x +1028. Find all critical points of f. For each critical point, determine whether it is a relative maximum, a relative minimum, or a saddle point of f

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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