1. Consider the general quadratic function f(u, v) = au² + 2buv + cv². (a) Characterize all extrema of f(u, v). Give a detailed answer. (b)Assuming A < 0, find the extrema of g(r, θ) = 2A(r – 1)² + 8A(r – 1)(θ + 2) + 8A(θ + 2)² (c) How can we employ the results in (a) for a general function with continuous first- and second-order partial derivatives?

1. Consider the general quadratic function f(u, v) = au² + 2buv + cv². (a) Characterize all extrema of f(u, v). Give a detailed answer. (b)Assuming A < 0, find the extrema of g(r, θ) = 2A(r – 1)² + 8A(r – 1)(θ + 2) + 8A(θ + 2)² (c) How can we employ the results in (a) for a general function with continuous first- and second-order partial derivatives?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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