首先，求解最小值的方法是找出函数的极值点。
由于这是一个分数形式的函数，因此要先将分数化为乘法形式－X^2-20X+400 / 40-X = -(X^2+20X-400) * (40/ (40-X)) 。
令导数为0得到极值点：
d/dX[-(x^2+20x-400) * (40/(40-x))] = 0 。
解得 x = 10 或 x = -4 ， 因此可以得出有两个极值点。
在这里不能直接使用解析法来计算最小值，需要使用数值法来实现。
在 X=-4 处可以直接代入原函数得到有 f(-4)=100 ；
在 X=10 处代入原函数可以得到 f(10)=25.5 ； ...
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