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9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) < 0 on (-∞,3), f'(3) does not exist, and f'(x) > 0 on (3, 0). (iii) f"(x) < 0 on (-∞0, 3) U (3, 6), f"(6) = 0, and f"(x) > 0 on (6, ). (iv) lim f(x) = 4 and lim f(x)= ∞. || -00

9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) < 0 on (-∞,3), f'(3) does not exist, and f'(x) > 0 on (3, 0). (iii) f"(x) < 0 on (-∞0, 3) U (3, 6), f"(6) = 0, and f"(x) > 0 on (6, ). (iv) lim f(x) = 4 and lim f(x)= ∞. || -00

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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9. Sketch a graph that has the following properties: (i) \( f \) is continuous on \( (-\infty, \infty) \). (ii) \( f'(x) < 0 \) on \( (-\infty, 3) \), \( f'(3) \) does not exist, and \( f'(x) > 0 \) on \( (3, \infty) \). (iii) \( f''(x) < 0 \) on \( (-\infty, 3) \cup (3, 6) \), \( f''(6) = 0 \), and \( f''(x) > 0 \) on \( (6, \infty) \). (iv) \( \lim_{x \to -\infty} f(x) = 4 \) and \( \lim_{x \to \infty} f(x) = \infty \).
Transcribed Image Text:9. Sketch a graph that has the following properties: (i) \( f \) is continuous on \( (-\infty, \infty) \). (ii) \( f'(x) < 0 \) on \( (-\infty, 3) \), \( f'(3) \) does not exist, and \( f'(x) > 0 \) on \( (3, \infty) \). (iii) \( f''(x) < 0 \) on \( (-\infty, 3) \cup (3, 6) \), \( f''(6) = 0 \), and \( f''(x) > 0 \) on \( (6, \infty) \). (iv) \( \lim_{x \to -\infty} f(x) = 4 \) and \( \lim_{x \to \infty} f(x) = \infty \).
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