CHAPTER X.
GEOMETRICAL MEANING OF DIFFERENTIATION.
It is useful to consider what geometrical meaning can be given to the differential coefficient.
In the first place, any function of , such, for example, as , or , or , can be plotted as a curve; and nowadays every schoolboy is familiar with the process of curve-plotting.
Fig. 7.
Let , in Fig. 7, be a portion of a curve plotted with respect to the axes of coordinates and . Consider any point on this curve, where the abscissa of the point is and its ordinate is . Now observe how changes when is varied. If