Example of a discontinuous function for which limit of the differential quotient exists in $\mathbb R\cup\{-\infty,+\infty\}$

Question

I am just asking this question for my verification of own answer. I have taken as example the function $f(x)=1/x$ if $x\neq 0$ and $0$ if $x=0$. Here $\lim_{x\to 0}\frac{f(x)-f(0)}{x-0}=+\infty$.Is this example correct? Note: I am also asking this question for sharing what I know or learn with other members in the community.

@Thomas I am just sharing my learning with the stackexchange community,I could also post it as answer to own question. — Kishalay Sarkar, Dec 23 '19 at 11:53
Somewhat related is $\alpha$-derivative (concept), and more related is a google search for "infinite derivative" + "Cantor function". — Dave L. Renfro, Dec 23 '19 at 13:47

score 1 · Accepted Answer · answered Dec 23 '19 at 12:04

1

It is correct. Note that an example of a continuous such function is $x\mapsto\sqrt[3]{x}$ at $x=0$.

answered Dec 23 '19 at 12:04

Martund

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Example of a discontinuous function for which limit of the differential quotient exists in $\mathbb R\cup\{-\infty,+\infty\}$

1 Answers1