# SOLVEDDifferentiability.

#### Sudharaka

Hi everyone,

Supppose f is a even differentiable function in R (real numbers). Then f ' is an odd function. But what can we say about the differentiability of f ' ?

Since we don't know the exsistance of $$\displaystyle \lim_{x\rightarrow{c}}\frac{f '(x)-f '(c)}{x-c}$$ for all $$\displaystyle c\in{R}$$ we cannot tell anything about the differentiability of f ' is'nt ?

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#### Drexel28

MHF Hall of Honor
Hi everyone,

Supppose f is a even differentiable function in R (real numbers). Then f ' is an odd function. But what can we say about the differentiability of f '' ?

Since we don't know the exsistance of $$\displaystyle \lim_{x\rightarrow{c}}\frac{f '(x)-f '(c)}{x-c}$$ for all $$\displaystyle c\in{R}$$ we cannot tell anything about the differentiability of f '' is'nt ?

You can't say anything.

• Sudharaka

#### Sudharaka

You can't say anything.
Dear Drexel28,

Thanks for the reply. However I have noticed that I had made a typo in my original post hence I corrected it. I want to know about the differentiability of f ' not f ''.

Sorry for the inconvenience caused.

#### Drexel28

MHF Hall of Honor
Dear Drexel28,

Thanks for the reply. However I have noticed that I had made a typo in my original post hence I corrected it. I want to know about the differentiability of f ' not f ''.

Sorry for the inconvenience caused.
My response still stands. Just because $$\displaystyle f$$ is even or odd and it's differentiable does not mean it's twice differentiable.

• Sudharaka