ensen's Inequality 4. Suppose that f is twice-differentiable on all of X. Prove that f is convex on X if and only if f"(x) > 0 for all x E X. >>

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Jensen's Inequality**

4. Suppose that \( f \) is twice-differentiable on all of \( X \). Prove that \( f \) is convex on \( X \) if and only if \( f''(x) \ge 0 \) for all \( x \in X \).

Note: There is a comment indicating uncertainty if this is actually a problem.
Transcribed Image Text:**Jensen's Inequality** 4. Suppose that \( f \) is twice-differentiable on all of \( X \). Prove that \( f \) is convex on \( X \) if and only if \( f''(x) \ge 0 \) for all \( x \in X \). Note: There is a comment indicating uncertainty if this is actually a problem.
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