| 单词 | second derivative |
| 释义 | second derivative The first derivative of the first derivative of a function. The first derivative measures a function's slope; the second derivative measures how the slope changes as the argument increases: that is, it measures the function's curvature. The second derivative of y = f(x) is written d2 y/dx2 ; alternatively, the first derivative can be written f′(x) and the second derivative can be written f″(x). If d2 y/dx2 > 0 the function is convex; if d2 y/dx2 < 0 the function is concave. At stationary values, where dy/dx = 0, if d2 y/dx2 < 0, y has a maximum, and if d2 y/dx2 > 0, y has a minimum. (NB while these are sufficient, they are not necessary conditions for a maximum or minimum of y.) |
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