Find and classify the stationary point(s) of the following functions: (a) 1: R³→ R defined by: 1(x) = x" Ax – 6" x, where: -1 1 2 A = 1 3 1 b = 1 1 -3 Is l a quadratic form? а

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 20E
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Find and classify the stationary point(s) of the following functions:
(a) l: R³→ R defined by:
1(x) = x" Ax - 6"x,
where:
3
-1
1
2
A =
1
3
1
b :
1
1
-3
8
Is l a quadratic form?
(b) m : R²→ R defined by:
m(x) – af + «} – 2a²u} – 3x2,
where a + 0.
Make sure to indicate whether the points you find are local or global extreme
points.
Transcribed Image Text:Find and classify the stationary point(s) of the following functions: (a) l: R³→ R defined by: 1(x) = x" Ax - 6"x, where: 3 -1 1 2 A = 1 3 1 b : 1 1 -3 8 Is l a quadratic form? (b) m : R²→ R defined by: m(x) – af + «} – 2a²u} – 3x2, where a + 0. Make sure to indicate whether the points you find are local or global extreme points.
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