Page:Calculus Made Easy.pdf/121

 Further Examples.

A most interesting example is afforded by a curve that has both a maximum and a minimum. Its equation is:

Now



Equating to zero, we get the quadratic,

and solving the quadratic gives us two roots, viz.

Now, when $$x=3$$, $$y=1$$; and when $$x=1$$, $$y=2\tfrac{1}{3}$$. The first of these is a minimum, the second a maximum.

The curve itself may be plotted (as in Fig. 28)