Page:Calculus Made Easy.pdf/96

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 $x$, 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.

Fig. 7.

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 $x$