y=x(80-2x)(40-2x)
=x(3200-80x-160x+4x²)
=x(3200-240x+4x²)
=3200x-240x²+4x³
y'=3200-480x+12x²
12x²-480x+3200=0
x²-40x=-800/3
x²-40x+400=400-800/3
(x-20)²=400/3
x-20=±20√3/3
x=20±20√3/3
x2≈8.453
长方形铁皮的四角各剪去一个边长为8.453cm的正方形,然后把四边向上折叠90°后焊接成的无盖长方体铁盒容积最大.