Page:Calculus Made Easy.pdf/48

Let us illustrate this example by working out the graphs of the equations $y=7x^{2}$ and ${\frac {dy}{dx}}=14x$, by assigning to $x$ a set of successive values, $0,1,2,3,$ etc., and finding the corresponding values of $y$ and of ${\frac {dy}{dx}}$.

These values we tabulate as follows:

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$-1$	$-2$	$-3$
$y$	$0$	$7$	$28$	$63$	$112$	$175$	$7$	$28$	$63$
${\tfrac {dy}{dx}}$	$0$	$14$	$28$	$42$	$56$	$70$	$-14$	$-28$	$-42$

Fig. 6.—Graph of $y=7x^{2}$.	Fig. 6a.—Graph of ${\frac {dy}{dx}}=14x$.

Now plot these values to some convenient scale, and we obtain the two curves, Fig. 6 and 6a.