Timeline for Positive Derivative
Current License: CC BY-SA 2.5
3 events
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| May 20, 2010 at 7:53 | comment | added | Pete L. Clark | Right, because then $f'$ is necessarily positive on an entire interval, not just at the point. Even in freshman calculus I try to make the distinction between "pointwise positivity" of $f'$ implies $f$ is increasing "through" the point -- i.e., smaller to the left, bigger to the right -- whereas "intervalwise positivity" implies increasing on an interval. I assumed this was part of the standard spiel. Now I wonder whether I am being too ambitious... | |
| May 19, 2010 at 15:26 | comment | added | Julián Aguirre | You just beat me. I would like to comment that f' is not continuous at 0. If we add the condition that f' be continuous at x_0, then f is increasing in an interval around x_0. | |
| May 19, 2010 at 15:15 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |