1. ## Derivative help

So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.

2. ## Re: Derivative help

Originally Posted by ethandf06
So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.
For that you can have piecewise functions(like ceil or floor) which are:

$f(x) = \lceil{x}\rceil \text{ or } g(x) = \lfloor{x}\rfloor$

continuous at $x = 1, 2, 3$ but not differentiable at these locations.

The plot is given below:

3. ## Re: Derivative help

Originally Posted by ethandf06
So I'm completely lost on this question and I'm not sure where to start any help would be greatly appreciated. Here is the question: find a function f(x) that is continuous at x=1,2 and 3 but not differentiable at x=1,2 and 3. Comment: it has to be one such function not three functions. Thanks for the help.
Here is such a function that is continuous everywhere.