| Popis: |
In the Classroom Note Proof of the mean value theorem (this MONTHLY, vol. 65, 1958, pp. 362-364), C. L. Wang uses a translation-rotation of the Cartesian coordinate system to obtain the Mean Value Theorem from Rolle's Theorem. The chief merit of this proof is that it provides a natural geometric motivation for the Mean Value Theorem. However, as the author points out, there are cases where his method of proof breaks down. This occurs whenever the graph of the given curve doubles back upon itself and is not the graph of a function in terms of the XY-coordinate system. (See Fig. 1 for example.) |
