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

These values we tabulate as follows:

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

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

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