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

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

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