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Is it true that the product of two convex functions f,g: R→ R is always convex? Prove or give a counterexample.

Is it true that the product of two convex functions f,g: R→ R is always convex? Prove or give a counterexample.

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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(d) Is it true that the product of two convex functions f, g: R R is always convex? Prove or give a counterexample.
Transcribed Image Text:(d) Is it true that the product of two convex functions f, g: R R is always convex? Prove or give a counterexample.
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