Is the Function x->|x| Differentiable at 0?

[losin]

I want to show x->abs(x) is not differentiable at 0

Some techniques in analysis are required... how should i do?

 

[Landau]

Calculate left and right limit of the difference quotient. If the function were differentiable, these would coincide, but they don't.

 

[g_edgar]

More basically ... use the definition of derivative.

 

[Landau]

The definition is the limit of the difference quotient.