| This research is integrated with the course the author carrying out in a higher vocational school, and aims at understanding and coping with the difficulties students experienced. The part of course included in this research is application of derivative, which can be divided into four parts:the mean value theorem, the judgment of monotonicity for differentiable functions, the (local/global) maxima and minima, and the concave and convex curves, During the research, the feedback is collect mainly via interview immediately after class, and test when each part is finished. The data is then evaluated for the design of the following lessons.The main feature of this chapter is the use of multiple representations, with its concepts or theorems introduced by graph while most of the problems students solve need symbolic calculation. As literature points out, the representation is a crucial factor in teaching mathematics.First, abstract mathematical objects and its relations cannot be expressed with out representation; second, different representations contain different information of the same object, or express the same information in different effectiveness, so the course must accommodate different representations to maximize student's understanding;third, the students must learn to separate objects from its representations. In this research, graphs play an important role in supporting students solving problems of monotonicity and extreme values, but means little while students solve problems related to mean value theorem. Because of that, it may be concluded that even the reasoning sutdents used during the lessons in this research can always be classified as imitative, the imitated procedures may makes sense to students when the graph and symbolic representations can link up closely.Based on the analyses, this article put forward its own idea about the instruction of application of derivative in higher vocational school.
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