| 单词 | local maximum |
| 释义 | local maximum A value of a function which is greater than at any nearby value of its argument, or set of values of its arguments. It is a necessary condition for a local maximum of y = f(x) that dy/dx = 0; provided this is satisfied, it is a sufficient condition for a local maximum that d2 y/dx2 < 0. A local maximum may also be a global maximum, if there is no value of x for which y is greater. This need not be the case, however: consider the function y = x3 - 3x. dy/dx = 0 when x2 = 1; and d2 y/dx2 = 6x. y has a maximum at x = -1, but this is only a local and not a global maximum, since y can be made indefinitely large by taking a large enough positive value of x. See also: maximum |
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