# Find a sequence of continuously differentiable functions

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

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