| 单词 | point of inflection |
| 释义 | point of inflection A point where a function changes its curvature. This means that its second derivative changes sign. For example, consider the function y = ax3 + bx, for which dy/dx = 3ax2 + b and d2 y/dx2 = 6ax. The sign of d2 y/dx2 thus changes when x = 0; if a > 0, d2 y/dx2 < 0 for negative x and d2 y/dx2 > 0 for positive x. y thus has a point of inflection at x = 0. This may not be a stationary value: in the case above y is stationary at x = 0 if and only if b = 0. |
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