# Give an example which is continous everywhere but not differentiable at 3 points?

Apr 12, 2017

$f \left(x\right) = \left\mid x - 1 \right\mid \cdot \left\mid x - 2 \right\mid \cdot \left\mid x - 3 \right\mid$

#### Explanation:

Here is what a graph of this function would look like:
graph{abs(x-1)abs(x-2)abs(x-3) [-0.13, 4.736, -0.249, 2.181]}
Although the function is defined for $\forall x \in \mathbb{R}$
it is not differentiable at $x \in \left\{1 , 2 , 3\right\}$