将函数单调性判定定理中函数在某个区间可导的条件减弱至Dini导数存在，并利用新的证明方法将原有定理的充分条件进行了推广，得到了新的充分条件、必要条件和充要条件。%The differentiable condition is weaken to the existence of Dini derivative, and by the new method, the original theorem is generalized, also some new sufficient condition, necessary condition and sufficient and necessary condition are obtained.
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