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For each of the following functions f(x) (x E R²), describe the sets V₁ ≥ 4 = { x | f(x) ≥ 4 } and V₁ ≤ 4 = { x | f(x) ≤ 4 } and show, by definition, which ones are convex: 2 2 a) f(x) = x₁² + x₂² c) f(x) = x₁ + x2 e) f(x) = X₁² b) f(x) = -x₁²x₂² d) f(x) = -X₁ - X2 2 f) f(x) -X₁²

For each of the following functions f(x) (x E R²), describe the sets V₁ ≥ 4 = { x | f(x) ≥ 4 } and V₁ ≤ 4 = { x | f(x) ≤ 4 } and show, by definition, which ones are convex: 2 2 a) f(x) = x₁² + x₂² c) f(x) = x₁ + x2 e) f(x) = X₁² b) f(x) = -x₁²x₂² d) f(x) = -X₁ - X2 2 f) f(x) -X₁²

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For each of the following functions f(x) (x E R²), describe the sets V₁2 4 = {x | f(x) ≥ 4 } and V₁ ≤ 4 = { x | f(x) ≤ 4} and show, by f definition, which ones are convex: a) f(x) = 2 2 x₁² + x₂² c) f(x) = x₁ + x₂ 2 e) f(x) = x₁² b) f(x) = = -x₁²x₂² d) f(x) = −X₁ - X2 2 f) f(x) = -x₁² 2
Transcribed Image Text:For each of the following functions f(x) (x E R²), describe the sets V₁2 4 = {x | f(x) ≥ 4 } and V₁ ≤ 4 = { x | f(x) ≤ 4} and show, by f definition, which ones are convex: a) f(x) = 2 2 x₁² + x₂² c) f(x) = x₁ + x₂ 2 e) f(x) = x₁² b) f(x) = = -x₁²x₂² d) f(x) = −X₁ - X2 2 f) f(x) = -x₁² 2
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