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For each of the following functions, show whether it is convex, concave, or neither. (a) f(x) = x² + 3x₁x₂ + x² (b) f(x)=x²-x₁x₂ - 2x² (c) f(x) = 3x₁ + 2x² + 4x₂ − 2x₁x₂ + x² - (d) For what values of a, b, and c will ax² + bx₁x₂ + cx2 be a convex? A concave function?

For each of the following functions, show whether it is convex, concave, or neither. (a) f(x) = x² + 3x₁x₂ + x² (b) f(x)=x²-x₁x₂ - 2x² (c) f(x) = 3x₁ + 2x² + 4x₂ − 2x₁x₂ + x² - (d) For what values of a, b, and c will ax² + bx₁x₂ + cx2 be a convex? A concave function?

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, show whether it is convex, concave, or neither. (a) f(x) = x² + 3x₁x₂ + x²² (b) f(x) = -x² − x₁x₂ - 2x² (c) f(x) = 3x₁ + 2x² + 4x₂ − 2x₁x₂ + x² (d) For what values of a, b, and c will ax² + bx₁x₂ + cx² be a convex? A concave function?
Transcribed Image Text:For each of the following functions, show whether it is convex, concave, or neither. (a) f(x) = x² + 3x₁x₂ + x²² (b) f(x) = -x² − x₁x₂ - 2x² (c) f(x) = 3x₁ + 2x² + 4x₂ − 2x₁x₂ + x² (d) For what values of a, b, and c will ax² + bx₁x₂ + cx² be a convex? A concave function?
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