A=-4x^2+40xx是窗帘的宽度,A是4个窗帘的面积.问宽度是多少的时候面积值最大?面积值是多少?TheamountofclothusedtomakefourcurtainsisgivenbythefunctionA=-4x^2+40x,wherexisthewidthofonecurtaininfeetand

Question

A=-4x^2+40x x是窗帘的宽度,A是4个窗帘的面积.问宽度是多少的时候面积值最大?面积值是多少?
The amount of cloth used to make four curtains is given by the function A=-4x^2+40x,where x is the width of one curtain in feet and A is the total area in square feet.Find the width that maximizes the area of the curtains.What is the maximum area?

Answer 1

A= -4x^2+40x
= -4(x^2-10x)
= -4(x^2-10x+25)+100
= -4(x-5)^2+100
因为 (x-5)^2有最小值0
所以 -4(x-5)^2有最大值0
所以 -4(x-5)^2+100有最大值100
即当x=5时,A有最大值100
答：宽度是5的时候面积值最大,面积值是100