Question

Where is the function |3x-1| not differentiable?

I know the answer is 1/3, but I'm looking for some explanation/clarification.

Answer 1

3x -1 = 0 add 1 to both sides
3x = 1 divide by 3 on both sides
x = 1/3

Answer 2

Is it then because for h's less than 0 the absolute value function is negative an for h's greater than 0 it's positive?

Answer 3

If you see the right of x=1/3 difeerential is +3 whereas to the left is -3. Hence it is not differentiable.