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Calculus Made Easy
readily see that the equation represents a curve with a minimum.
These values are plotted in Fig. 26, which shows that has apparently a minimum value of , when is made equal to . But are you sure that the minimum occurs at , and not at or at ?
Of course it would be possible with any algebraic expression to work out a lot of values, and in this way arrive gradually at the particular value that may be a maximum or a minimum.
Fig. 27.
Here is another example:
Let
.
Calculate a few values thus: