MAXIMA AND MINIMA
101
Further Examples.
A most interesting example is afforded by a curve that has both a maximum and a minimum. Its equation is:
.
Now
.
Fig. 28.
Equating to zero, we get the quadratic,
;
and solving the quadratic gives us two roots, viz.
Now, when , ; and when , . The first of these is a minimum, the second a maximum.
The curve itself may be plotted (as in Fig. 28)