將長(zhǎng)方形圍成圓柱體后,長(zhǎng)方形的兩條邊分別為圓柱體的高和底面周長(zhǎng)：
設(shè)所圍成的圓柱體的高為x,其中0＜x≤10
則底面周長(zhǎng)=(20÷2)-x=10-x
底面半徑為 = (10-x)/(2π)
圓柱體積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)
當(dāng)x∈（0,10/3）時(shí),V'＞0,V單調(diào)增；x∈（10/3,10）時(shí),V'＜0,V單調(diào)減
當(dāng)x=10/3時(shí),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)怎么算的對(duì)V = (x^3-20x^2+100x) /(4π) 求導(dǎo)數(shù)：V' = 1/(4π)(3x^2-40x+100)= 1/(4π) (3x-10)(x-10)【分解因式】= 3/(4π) (x-10/3)(x-10)