1. ## Countinous after derivative

If a function $\displaystyle f$is countinous on the closed interval $\displaystyle (a,b)$ and diffrenciable on the open interval $\displaystyle (a,b)$. Then $\displaystyle f'$ is countinous on the closed interval $\displaystyle [a,b]$. It seems true, I was not able to find any counterexamples.

2. Originally Posted by ThePerfectHacker
If a function $\displaystyle f$is countinous on the closed interval $\displaystyle (a,b)$ and diffrenciable on the open interval $\displaystyle (a,b)$. Then $\displaystyle f'$ is countinous on the closed interval $\displaystyle [a,b]$. It seems true, I was not able to find any counterexamples.
I may have the wrong end of the stick here but what about:

$\displaystyle f(x)=\sqrt x,\ x \in [0,1]\ ?$

RonL

3. Originally Posted by CaptainBlack
I may have the wrong end of the stick here but what about:

$\displaystyle f(x)=\sqrt x,\ x \in [0,1]\ ?$

RonL
"Wrong end of the stick" is that supposed to be a pun
Well, it is true that the endpoint is not countinous (end of stick) okay thus, what about the open interval?

4. Originally Posted by ThePerfectHacker
"Wrong end of the stick" is that supposed to be a pun
Well, it is true that the endpoint is not countinous (end of stick) okay thus, what about the open interval?
Not sure what you mean. It's a counter example; its continuous on a closed
interval $\displaystyle [0,1]$, differentiable on $\displaystyle (0,1)$, but its derivative is not continuous
on $\displaystyle [0,1]$.

RonL

5. I agree with you,

but what about if discountinous on an open interval? Is that possible?