SOLVED Differentiability.

Dec 2009
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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 ?

Your ideas are welcome......
 
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Drexel28

MHF Hall of Honor
Nov 2009
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1,566
Berkeley, California
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 ?

Your ideas are welcome......
You can't say anything.
 
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Dec 2009
872
381
1111
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
Nov 2009
4,563
1,566
Berkeley, California
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.
 
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