- #1
l'Hôpital
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- 0
So, a certain discussion occurred in class today...
If f is differentiable, is f ' continuous?
At first sight, there seems no reason to think so. However, we couldn't think any counterexample. It also seems logical that f' is continuous since otherwise f wouldn't be differentiable.
For example, suppose f(x) = ln x, for x > 0
Then f'(x) = 1/x. Yes, this is discontinuous, but it's not for the domain x > 0.
So, the question remains:
If f is differentiable, is f ' continuous?
If f is differentiable, is f ' continuous?
At first sight, there seems no reason to think so. However, we couldn't think any counterexample. It also seems logical that f' is continuous since otherwise f wouldn't be differentiable.
For example, suppose f(x) = ln x, for x > 0
Then f'(x) = 1/x. Yes, this is discontinuous, but it's not for the domain x > 0.
So, the question remains:
If f is differentiable, is f ' continuous?