Wednesday, January 30, 2019

calculus - Can function be differentiable but not continuous?

Is there any possible function that is not continuous but differentiable?



For example these functions, f(x)=πx+π whenever x<0 ,and f(x)=arctanπx when 0x.




I know that these are not continuous but when I derivative them, they get the same answers. Should I consider that differentiable or not?

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