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13. Let I be an interval and let f :1 R be differentiable on I. Show that if f' is positive on I, then f is strictly increasing on I. 14. Let I be an interval and letf : I R be differentiable on I. Show that if the derivative f is never 0 on I, then either f'(x) > 0 for all x EI or f'(x) < 0 for all xE I.

13. Let I be an interval and let f :1 R be differentiable on I. Show that if f' is positive on I, then f is strictly increasing on I. 14. Let I be an interval and letf : I R be differentiable on I. Show that if the derivative f is never 0 on I, then either f'(x) > 0 for all x EI or f'(x) < 0 for all xE I.

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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13. Let I be an interval and let f :1 R be differentiable on I. Show that if f' is positive on I, thenf is strictly increasing on I. 14. Let I be an interval and letf : I R be differentiable on I. Show that if the derivative f' is never 0 on I, then either f' (x) > 0 for all x EI or f'(x) < 0 for all xE I. 15 Let Ibe an interval Prove thot if fin
Transcribed Image Text:13. Let I be an interval and let f :1 R be differentiable on I. Show that if f' is positive on I, thenf is strictly increasing on I. 14. Let I be an interval and letf : I R be differentiable on I. Show that if the derivative f' is never 0 on I, then either f' (x) > 0 for all x EI or f'(x) < 0 for all xE I. 15 Let Ibe an interval Prove thot if fin
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