单词 | first-order conditions |
释义 | first-order conditions The conditions for a function to take a stationary value. If y = f (x), the first-order condition for a stationary value is dy/dx = fx = 0. For a function of several variables, y = f (x1, x2, …, xN) the first-order conditions for a stationary value are ∂y/∂xi = fi = 0 for each i. First-order conditions give necessary but not sufficient conditions for a maximum or minimum. It is necessary to go on to consider second- or higher-order conditions to check whether a stationary value of a function of one variable is a maximum, a minimum, or a point of inflection, and whether a stationary value of a function of several variables is a maximum, a minimum, or a saddle point. |
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