Another fun one is the slippery devil's staircase, Minkowski's question-mark function. It's strictly increasing but the derivative is 0 at rational numbers. ht

Another fun one is the slippery devil's staircase, Minkowski's question-mark function. It's strictly increasing but the derivative is 0 at rational numbers. https://en.wikipedia.org/wiki/Minkowski%27s_question-mark_function https://en.wikipedia.org/wiki/Minkowski%27s_question-mark_fu...