讨论了函数的介值性与连续性之间的相互关系以及导函数的介值性。

This paper intends to discuss the relation of the intermediate-value property and continuity of a function and point out the intermediate-value property of derivatives.

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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。

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.

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给出了导数的介值定理的内容，并用不同的方法对定理进行了严格的证明。

The content of intermediate value theorem of the derivative is given and strictly proved by using various methods.

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