A function f: R → R has a third order continuous derivative. Show that f(a) f'(a). f"(a). f"" (a) ≥ 0 for some a ER. .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A function \( f : \mathbb{R} \to \mathbb{R} \) has a third order continuous derivative. Show that

\[
f(a) \cdot f'(a) \cdot f''(a) \cdot f'''(a) \geq 0
\]

for some \( a \in \mathbb{R} \).
Transcribed Image Text:A function \( f : \mathbb{R} \to \mathbb{R} \) has a third order continuous derivative. Show that \[ f(a) \cdot f'(a) \cdot f''(a) \cdot f'''(a) \geq 0 \] for some \( a \in \mathbb{R} \).
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