Page:Calculus Made Easy.pdf/122

from the values calculated, as below, from the original equation.

$x$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$-4{\tfrac {1}{3}}$	$1$	$2{\tfrac {1}{3}}$	$1{\tfrac {2}{3}}$	$1$	$2{\tfrac {1}{3}}$	$7{\tfrac {2}{3}}$	$19$

A further exercise in maxima and minima is afforded by the following example:

The equation to a circle of radius $r$, having its centre $C$ at the point whose coordinates are $x=a$, $y=b$, as depicted in Fig. 29, is:

$(y-b)^{2}+(x-a)^{2}=r^{2}$.

This may be transformed into

$y={\sqrt {r^{2}-(x-a)^{2}}}+b$.

Fig. 29.

Now we know beforehand, by mere inspection of the figure, that when $x=a$, $y$ will be either at its maximum value, $b+r$, or else at its minimum value, $b-r$. But let us not take advantage of this