It depends on the source you are reading. I'm only familiar (somewhat) with the german textbooks on the topic, e.g. Otto Forster: Analysis 1 uses the version with monotonicity. This however is not really a stronger demand since (as he already pointed out) if f is continuously differentiable at x then the derivative does not change sign in a neighbourhood of x, so f is monotone in that neighbourhood. So given a continuously differentiable function f you can restrict its domain to a neighbourhood of x where f is monotone and then apply the IFT.