EDB — 1CD

[1CD] Prerequisites:[1C8]↺↻.Difficulty:*.

Find a bounded function $f:ℝ\to ℝ$ that maps intervals into intervals, but such that there does not exist $g:ℝ\to ℝ$ differentiable at every point and with $f=g^{\prime }$.

(Note that $f$ cannot be continuous, due to the Fundamental Theorem of Calculus.)