Wednesday, March 13, 2019

calculus - Continuity of 'derivative of a function'

I just learn one theorem which says If "$f^{'}$ exists and is monotonic on an open interval (a,b),then $f^{'}$ is continuous on (a,b)."I got the proof but now I am looking for one example in which if I relaxe the hypothesis of monotonic-ness then resulting $f^{'}$ is not continuous.I am thinking but unable to get such example. Thanks.

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analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...