EDB — 1CD

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

Find a bounded function \(f:ℝ→ℝ\) that maps intervals into intervals, but such that there does not exist \(g:ℝ→ℝ\) differentiable at every point and with \(f=g'\).

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