[WolframAlpha]Local minima有误

hbghlyj

kuing 发表于 2017-9-10 10:07
很简单啊，首先通过消元后求导（又或者用拉格朗日乘数）算一下极值点，发现极值点有负数，可见最值只能在边 ...

几何上，到两个平面的距离的乘积，没有极值点，但WolframAlpha出错
\begin{split}f&=(x+3y+5z)\left(x+\frac{y}{3}+\frac{z}{5}\right)\\
&=\left(x+3y+5(1-x-y)\right)\left(x+\frac{y}{3}+\frac{1-x-y}{5}\right)\\
&=(-4x-2y+5)\left(\frac{x}{5}+\frac{y}{15}+\frac{1}{5}\right)\end{split}
$x\to-\infty,y=0$时$f\to-\infty$
import graph3;unitsize(1cm);

currentprojection = perspective((1,2,.5));

real f1(pair z) {
  return -(z.x + 3z.y)/5;
}

real f2(pair z) {
  return -5*(z.x + z.y/3);
}

draw(surface(f1,(-2,-2),(2,2)),lightgray,meshpen=black+thick());
draw(surface(f2,(-1,-1),(1,1)),lightgray,meshpen=black+thick());
axes3(red,Arrow3);

hbghlyj

1. ResourceFunction["GlobalMinima"][{(x+3 y+5 z) (x+y/3+z/5),x+y+z==1},{x,y,z}]

复制代码

输出{}