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/etc/nginx/nginx.conf.如图,一张边长为20cm正方形硬纸板,把它的四个角都剪去一个边长为xcm的小正方形,然后把它折成一个无盖的长方体,设长方体的容积为Vcm3,请回答下列问题:(1)若用含有x的代数式表示V,则V=x(20-2x)2.(2)根据(1)中结果,填写下表:x(cm)1234567V(cm3)324512500384252(3)观察(2)中表格,容积V的值是否随x值的增大而增大?此时当x取什么整数值时,容积V的值最大?(4)课后小英同学继续对这个问题作了以下探究:当x=3.2cm时,V=591.872cm3;当x=3.3cm时,V=592.548cm3;当x=3.4cm时,V=592.416cm3;当x=3.5cm时,V=591.5cm3,小英同学发现x的取值一定介于3.3cm~3.4cm之间,估计x的取值还能更精确些,小英再计算x=3.3cm,3.33cm,3.333cm,3.3333cm…时,发现容积还在逐渐增大.现请你也观察(4)中数据变化,能否推测x可以取到哪一个定值,容积V的值最大?(直接写出即可)
解:(1)根据题意,无盖的长方体的底面正方形的边长为20-2x,高为x,∴V=x(20-2x)2;(2)在V=x(20-2x)2中,当x=3时,V=3×(20-2×3)2=3×196=588,当x=4时,V=4×(20-2×4)2=4×144=576,(3)观察上表,可以发现容积V的值不是随着x的值的增大而增大的,从表中可知,当x取整数3时,容积V最大;(4)根据小英的x的取值,x无限接近3,∴当x=3时,容积V的值最大,最大值约为592.593.(1)表示出底面正方形的边长,然后根据体积公式解答;(2)根据(1)中得出的关系式,代入数据x=3、4进行计算即可得到对应的V的值;(3)根据表格数据的变化规律即可得解;(4)根据小英取的x的值的特点即可得解.}

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