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OpenStudy (loki):

Does the derivative for |x| not exist at 0?

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OpenStudy (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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (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.

OpenStudy (anonymous):

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

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OpenStudy (anonymous):

The derivative does not exist at sharp corners or cusps

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