(a) Find all local extrema of the function f(x, y, z) = yz − 3x² – 2x³. You do NOT need to classify them. (b) Find the global extrema of f on the unit sphere x² + y² + z² = 1. (Hint: Use Lagrange multipliers.) (c) Find the global extrema of f on the closed unit ball x² + y² + z² ≤ 1.
(a) Find all local extrema of the function f(x, y, z) = yz − 3x² – 2x³. You do NOT need to classify them. (b) Find the global extrema of f on the unit sphere x² + y² + z² = 1. (Hint: Use Lagrange multipliers.) (c) Find the global extrema of f on the closed unit ball x² + y² + z² ≤ 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.1: Parabolas
Problem 40E
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Transcribed Image Text:3. (a) Find all local extrema of the function f(x, y, z) = yz — 3x² – 2x³. You do NOT
need to classify them.
(b) Find the global extrema of f on the unit sphere x² + y² + z² = 1. (Hint: Use
Lagrange multipliers.)
(c) Find the global extrema of f on the closed unit ball x² + y² + z² ≤ 1.
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