Find all critical points of the the functionF(x,y)=ln(x2 +y2 +2y+2)in the domain D = {(x,y) ; x2 + y2 < 16}, and decide if each is a local minimum, local maximum or saddle point. 4. Find all critical points of the the functionF(x, y) = In(x² + y² + 2y + 2)in the domain D{(x,y) ; x? + y? < 16}, and decide if each is a local minimum,local maximum or saddle point.

Given function is- F(x,y)=ln(x2+y2+2y+2) Domain is D=(x,y);x2+y2<16 We need to determine…

Answered: Find all critical points of the the…

Find all critical points of the the function F(x,y)=ln(x2 +y2 +2y+2) in the domain D = {(x,y) ; x2 + y2 < 16}, and decide if each is a local minimum, local maximum or saddle point.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Question

Find all critical points of the the function
F(x,y)=ln(x2 +y2 +2y+2)

in the domain D = {(x,y) ; x2 + y2 < 16}, and decide if each is a local minimum, local maximum or saddle point.

4. Find all critical points of the the function
F(x, y) = In(x² + y² + 2y + 2)
in the domain D
{(x,y) ; x? + y? < 16}, and decide if each is a local minimum,
local maximum or saddle point.

Formula Formula A function f ( x ) is also said to have attained a local minimum 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 a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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