将长方形围成圆柱体后,长方形的两条边分别为圆柱体的高和底面周长：
设所围成的圆柱体的高为x,其中0＜x≤10
则底面周长=(20÷2)-x=10-x
底面半径为 = (10-x)/(2π)
圆柱体积V = π*[(10-x)/(2π)]^2*x = x(x-10)^2 /(4π) = (x^3-20x^2+100x) /(4π)
V' = 1/π (3x^2-40x+100) = 3/(4π) * (x-10/3)(x-10)
当x∈（0,10/3）时,V'＞0,V单调增；x∈（10/3,10）时,V'＜0,V单调减
当x=10/3时,V取最大值：
Vmax = x(x-10)^2 /(4π) = 10/3*(10/3-10)^2 /(4π) = 1000/(27π)V' = 1/π (3x^2-40x+100) = 3/(4π) *(x-10/3)(x-10)怎么算的对V = (x^3-20x^2+100x) /(4π) 求导数：V' = 1/(4π)(3x^2-40x+100)= 1/(4π) (3x-10)(x-10)【分解因式】= 3/(4π) (x-10/3)(x-10)