CHAPTER XI.
MAXIMA AND MINIMA.
One of the principal uses of the process of differentiating is to find out under what conditions the value of the thing differentiated becomes a maximum, or a minimum. This is often exceedingly important in engineering questions, where it is most desirable to know what conditions will make the cost of working a minimum, or will make the efficiency a maximum.
Now, to begin with a concrete case, let us take the equation
.
Fig. 26.
By assigning a number of successive values to , and finding the corresponding values of , we can