Consider the function f(x,y) = 4x / x2+y2+4 a.) List all critical points of f(x,y). b.) List all critical points of f(x,y) which are local maxima. c.) List all critical points of f(x,y) which are local minima. d.) List all critical points of f(x,y) which are saddlepoints.

Consider the function f(x,y) = 4x / x2+y2+4 a.) List all critical points of f(x,y). b.) List all critical points of f(x,y) which are local maxima. c.) List all critical points of f(x,y) which are local minima. d.) List all critical points of f(x,y) which are saddlepoints.

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

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Consider the function f(x,y) = 4x / x²+y²+4

a.) List all critical points of f(x,y).

b.) List all critical points of f(x,y) which are local maxima.

c.) List all critical points of f(x,y) which are local minima.

d.) List all critical points of f(x,y) which are saddlepoints.

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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