The existence of the so-called monotone increasing interval, from the above point of view, the constant is also monotonous, but here, this function can't be constant in a certain interval, so if you f'(x)=0 at this time, the x you get must be just some isolated points, not an interval, which actually doesn't meet the requirements of the topic;

Therefore, if a monotone interval is required, the point where f'(x)=0 must be the endpoint of the interval, and there must be f' (x) >; 0, so the necessary and sufficient condition of monotonically increasing interval is f' (x) >; 0, regardless of the endpoint of the domain.