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I know that [itex]e^{rx}[/itex] is an infinitely differentiable function.

However, say you have f= x. this is clearly one time differentiable, giving 1. a second time it can be derived as well, giving 0. is 0 differentiable, indeed differentiation gives zero.

So when is a function non-differentiable. i'm thinking of cusps, such as on x=0 with the function f=|x|, or other functions where the derivative is undefined. correct? are there other cases? it would also be interesting to see a function that is only finitely differentiable.

However, say you have f= x. this is clearly one time differentiable, giving 1. a second time it can be derived as well, giving 0. is 0 differentiable, indeed differentiation gives zero.

So when is a function non-differentiable. i'm thinking of cusps, such as on x=0 with the function f=|x|, or other functions where the derivative is undefined. correct? are there other cases? it would also be interesting to see a function that is only finitely differentiable.

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