| 单词 | local minimum |
| 释义 | local minimum A value of a function which is lower than at any nearby value of its argument, or set of values of its arguments. It is a necessary condition for a local minimum of y = f(x) that dy/dx = 0; provided this is satisfied, it is a sufficient condition for a local minimum that d2 y/dx2 > 0. A local minimum may also be a global minimum, if there is no value of x for which y is lower. 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 as a minimum at x = 1, but this is only a local and not a global minimum, since y can be made negative and indefinitely large by taking a large enough negative value of x. See also: maximum |
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