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. .
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
Section: Chapter Questions
Problem 1RQ
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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 \( a \in \mathbb{R} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2Fad11e7aa-c4da-4c39-b184-965798e2c523%2Fejvn28a_processed.png&w=3840&q=75)
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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