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《通报》83年第8期发表了陆俊杰干同志“关于微分中值定理教学的一点看法”的文章,提出了用演绎、推理的方法,求所需的辅助函数,但从另一个角度,学生很自然的想到微分中值定理与洛尔定理仅是区间端点函数值相等与不相等的区别,能否通过旋转变换去解决这个问题呢?!我们从旋转变换的图形不变性可知:通过旋转变换满足洛尔定理的条件的,而且旋转的坐标轴显然是平行于直线y=(f(b)-f(a)/b-a)x的,因此,得出微分中值定理的又一证明。
In the eighth edition of the “Announcement”, published in the eighth issue of Comrade Lu Junjie’s “A View on Differential Mean Value Theorem Teaching”, he proposed the use of deductive and inferential methods to find the required auxiliary functions, but from another perspective, Students naturally think that the differential mean value theorem and Rolle’s theorem are only the differences between the equal and unequal values of the interval endpoint functions. Can we solve this problem through the rotation transformation? We know from the invariance of the rotation transformation graph: through rotation The transformation satisfies the conditions of Lohr’s theorem, and the axis of rotation is apparently parallel to the straight line y=(f(b)-f(a)/ba)x, so another proof of the differential mean value theorem is obtained.