Question

Construct a function f: R--> R that is differentiable at x =-1,0,1 and at no other point
Please, help

Answer 1

If f is diff. at x =-1,0,1, f is continuous at those points
Hence the piecewise function will be constructed under the form of
\(f(x) = \begin{cases}h(x)~~if~~~x\in A\\g(x)~~if~~x\in ~~~B\end{cases}\)

Answer 2

\(\huge\color{green}{{\rm BEST }~\rm of~luck !! :)}\)

Answer 3

try looking at the following for starters

\[f(x) = \begin{cases}0~~if~~~x\in \mathbb{R}\backslash\mathbb{Q}\\x^2~~if~~x\in\mathbb{Q}\end{cases}\]