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[几何] 三次函数上任意两点的中点的集合

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hbghlyj Posted at 2024-4-12 22:19:44 |Read mode

$y=x^3-x$上任意两点的中点的集合是整个平面吗？

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Author| hbghlyj Posted at 2024-4-12 22:33:35

是平面被$y=x^3-x$的图象和y轴划分的区域

$$x(y-(x^3-x))>0$$
也可以写成\[
\frac{y}{x}>x^2-1
\]
Discriminant[(2x-t)^3-(2x-t)-(2y-t^3+t),t]>0

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