knowledge; let us set about finding what value of will make a maximum or a minimum, by the process of differentiating and equating to zero.
,
which reduces to
.
Then the condition for being maximum or minimum is:
.
Since no value whatever of will make the denominator infinite, the only condition to give zero is
.
Inserting this value in the original equation for the circle, we find
;
and as the root of is either or , we have two resulting values of ,
The first of these is the maximum, at the top; the second the minimum, at the bottom.