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Hello can you help me with this question?

Given an example of a sequence of continuity differentiable functions $\{f_n\}$ on $[0,1]$ so that $f_n\rightarrow f$ uniformly but $f$ is not differentiable at all points of $[0,1]$. $Hint$: draw graphs first.

I thought a good answer would be $f(x)$ = $|x|$ where $f_n(x)$= $x(1+1$/$n)$ but I wanted to take your opinion as well

Thanks

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  • $\begingroup$ No, it doesn't work. $|x| = x$ on $[0,1]$, so that $f$ is still differentiable. $\endgroup$ – zoidberg Dec 7 '18 at 6:59
  • $\begingroup$ Please retype the question in the image for the convenience! $\endgroup$ – Le Anh Dung Dec 7 '18 at 6:59
  • $\begingroup$ Your general idea of trying to make a $V$-shaped limit is a good one though. $\endgroup$ – zoidberg Dec 7 '18 at 7:01
  • $\begingroup$ $f$ needs to be not differentiable at all points. $\endgroup$ – copper.hat Dec 7 '18 at 7:37
  • $\begingroup$ the Weierstrass function? $\endgroup$ – Lau Dec 7 '18 at 8:04

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