Page:Calculus Made Easy.pdf/96



is useful to consider what geometrical meaning can be given to the differential coefficient.

In the first place, any function of $$x$$, such, for example, as $$x^2$$, or $$\sqrt x$$, or $$ax+b$$, can be plotted as a curve; and nowadays every schoolboy is familiar with the process of curve-plotting.



Let $$PQR$$, in Fig. 7, be a portion of a curve plotted with respect to the axes of coordinates $$OX$$ and $$OY$$. Consider any point $$Q$$ on this curve, where the abscissa of the point is $$x$$ and its ordinate is $$y$$. Now observe how $$y$$ changes when $$x$$ is varied. If $$x$$