Differentiating, we get:
.
Now equate this to zero, thus:
.
Solving this equation for , we get:
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Now, we know that the maximum (or minimum) will occur exactly when .
Putting the value into the original equation, we get
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Now look back at Fig 26, and you will see that the minimum occurs when , and that this minimum of .
Try the second example (Fig. 24), which is
.
Differentiating,
.
Equating to zero,
,
whence
;
and putting this value of into the original equation, we find:
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This gives us exactly the information as to which the method of trying a lot of values left us uncertain.