N.B.–For the particular value of that makes a minimum, the value of .
If a curve first ascends and then descends, the values of will be positive at first; then zero, as the summit is reached; then negative, as the curve slopes downwards, as in Fig. 16. In this case is said to pass by a maximum, but the maximum value of is not necessarily the greatest value of . In Fig. 28, the maximum of is , but this is by no means the greatest value can have at some other point of the curve.
Fig. 16. |
Fig. 17. |
N.B.–For the particular value of that makes a maximum, the value of .
If a curve has the peculiar form of Fig. 17, the values of will always be positive; but there will be one particular place where the slope is least steep, where the value of will be a minimum; that is, less than it is at any other part of the curve.