Timeline for Why do we teach calculus students the derivative as a limit?
Current License: CC BY-SA 2.5
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| Apr 3, 2011 at 21:22 | comment | added | Toby Bartels | This also has the technical problem of not covering the case when a function is differentiable but not continuously so. (Of course, this might appear in a context where one is uninterested in such functions.) We can fix this by making it slightly more complicated: ask whether $\Delta{f}(a,-)$, the restriction of $\Delta{f}$ to a given vertical line $\{x = a\}$, admits a continuous extension; if so, then this is unique, and we define $f'(a)$ to be the new value $\Delta{f}(a,a)$. | |
| Jan 27, 2011 at 16:14 | comment | added | Thierry Zell | It's an interesting alternative to the usual, but ultimately I'm afraid it's even more challenging than the usual one. Of course, here I'm not talking about using the definition to perform computations, but even to grasp the intuitive meaning, resorting to functions of two variables strikes me as more than a student can comfortably handle. | |
| Jan 26, 2011 at 6:28 | history | answered | Patrick I-Z | CC BY-SA 2.5 |