The graph of modulus function is continuous

having a corner at x=0. It means that graph is differentiable at all points except at x=0 (we can not draw a tangent at a corner). ... Modulus function is a non – negative value.

How do you know if a modulus function is differentiable?

4 Answers. Hint: Near 0, x−1<0 and therefore f(x)=|x|−(x−1)=|x|−x+1. Use the definition of a derivative as a limit f′(x)=limh→0f(x+h)−f(x)h. Show that the left limit (negative h) differs from the right limit (positive h).

Why modulus function is not differentiable?

The left limit does not equal the right limit, and therefore the limit of the difference quotient of f(x) = |x| at x = 0 does not exist. Thus the absolute value function is not differentiable at x = 0. ... So, for example, take the absolute value function f(x) = |x| and restrict it to the closed interval [−1, 2].