This paper gives some properties of several special function discontinuity point and the first kind discontinuity point of ordinary real function. and points out their ap-plicaion in actual problems.
本文给出了几类常见函数间断点及一般实函数第一类间断点的某些特性，并指出它们在实际问题中的应用。
The paper discussed the characters of derivatives that it has the character of intermediate value property and it has no the character of the discontinuity points of the first kind.
讨论导函数的若干性质：导函数具有介值性、导函数无第一类间断点。
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