Timeline for existence of antiderivatives of nasty but elementary functions
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2010 at 12:33 | comment | added | Quimey | I want to say that there is a necessary condition in order to be the derivative of a derivable function defined in the interval (a,b). This condition is the intermediate value condition. I never use what you say, maybe I just misstated because I am not a native English speaker. I don't understand what is wrong in my post. Could you be more explicit please? | |
| Mar 12, 2010 at 12:24 | history | edited | Quimey | CC BY-SA 2.5 |
added 4 characters in body
|
| Mar 12, 2010 at 4:02 | comment | added | Qiaochu Yuan | The derivative of the integral of an integrable function need not exist everywhere. The obvious example is, for example, a step function. (The fundamental theorem of calculus as it is usually stated only applies to continuous integrands!) | |
| Mar 11, 2010 at 21:54 | history | edited | Quimey | CC BY-SA 2.5 |
added 357 characters in body; deleted 1 characters in body; deleted 94 characters in body
|
| Mar 11, 2010 at 21:22 | comment | added | Gerald Edgar | If a function is differentiable everywhere in an interval, then the derivative has the intermediate value property. Defined "everywhere except one point" is not good enough. This example is defined everywhere except one point. | |
| Mar 11, 2010 at 21:21 | comment | added | Yemon Choi | Darboux's theorem requires conditions on the function. So what you say is incomplete (sorry to nitpick, but the difference between "a reasonable-sounding function" and "any function" is vast). | |
| Mar 11, 2010 at 19:47 | history | answered | Quimey | CC BY-SA 2.5 |