What Are Some Examples of Unique Real Analysis Functions?

[gordon_0451]

Homework Statement

Please give examples

-functions continuous nowhere, continuous at one point

– functions differentiable everywhere but with discontinuous derivative

– Examples of uniformly continuous functions, functions not uniformly continuous

– Combinations of the above. For example, find a function, f : [0, 1] ! [0, 1], having the
intermediate-value property but continuous at only one point

thank you very much!

Homework Equations

Rolle’s theorem
Mean-value theorem
Cauchy mean-value theorem

The Attempt at a Solution

I have trouble to start it . Please help.

 

[lanedance]

hi gordon_0451, welcome to PF - you need to show your attempts & people will try & help