Page:Calculus Made Easy.pdf/123

 knowledge; let us set about finding what value of $$x$$ will make $$y$$ a maximum or a minimum, by the process of differentiating and equating to zero.

which reduces to

Then the condition for $$y$$ being maximum or minimum is:

Since no value whatever of $$x$$ 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 $$r^2$$ is either $$+r$$ or $$-r$$, we have two resulting values of $$y$$,

The first of these is the maximum, at the top; the second the minimum, at the bottom.