4 ms·
The standard definition of a derivative c involves the assumption that f is defined at c. However, you could also (probably) define the derivative as lim_{h->0
by smokedetector1 2y ago
The standard definition of a derivative c involves the assumption that f is defined at c.
However, you could also (probably) define the derivative as lim_{h->0} (f(c+h) - f(c-h))/2h, so without needing f(c) to be defined. But that's not standard.
- deleted 2y ago[deleted]
- JadeNB 2y ago> However, you could also (probably) define the derivative as lim_{h->0} (f(c+h) - f(c-h))/2h, so without needing f(c) to be defined. But that's not standard. Although this gives the right answer whenever f is differentiable at c, it can wrongly think that a function is differentiable when it isn't, as for the absolute-value function at c = 0.
- smokedetector1 2y agoGood point. So this is probably one of the reasons why the version I stated isn't used.
- JadeNB 2y agoIt is used, just with the caveat in mind that it may exist when the derivative doesn't. It is usually called the symmetric derivative (https://en.wikipedia.org/wiki/Symmetric_derivative https://en.wikipedia.org/wiki/Symmetric_derivative).
- deleted 2y ago[deleted]