For a while I've assumed that if a function is always strictly increasing, its derivative will always be positive. But that seems to be false and that its derivative can also be 0. Take f(x)=x^3 with f'(x)=3x^2 as an example. This function is always strictly increasing but for x=0
f'(0)=0. This would proboably make more sense if the function was increasing. I need some explaination on this.