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......

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......

Last edited: