## loki 5 years ago Does the derivative for |x| not exist at 0?

1. anonymous

@loki, you should consider the derivative from the left side and the derivative from the right side. consider those, then reconsider the idea of derivative of |x| at 0

2. anonymous

$$f \left( x \right) = \left| x \right|, f \prime(x)$$

3. anonymous

from the right, the function resembles y=x, from the left y=-x

4. anonymous

Yes, the derivative of |x| does not exist at zero, look guy when we draw the graph of it you will have a sharp point at the origin differentiability guarantees the smooth points remember the surface of the jack fruit.

5. anonymous

you can draw as many tangent line at x=0, that's why at x=0,|x| is not differentiable.

6. anonymous

The derivative does not exist at sharp corners or cusps