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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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