英文应用题.A rectangle has its base on the x-axis and it's two up

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/14 05:46:53

英文应用题.
A rectangle has its base on the x-axis and it's two upper corners on the parabola y=12-x^2.What is the largest possible area of the rectangle.
答案写着长方形的高是12-x^2,底边2x请问高和底边是怎么来的?

◆题目的意思是：有一个矩形,其底在X轴上,它上部的两个角尖在抛物线 y=12-x^2 上,问这个矩形可能围成的最大面积是多少?
你将这个方程的抛物线画出来,就能看到它是一个对称于Y轴,两边向X 轴渐落的扣碗形曲线.矩形在Y轴两边对称分布,所以矩形的底边长度是2X,
的上部两个点在抛物线 y=12-x^2 上,所以矩形的高是y=12-x^2.
◆继续帮你解题吧：
矩形的面积S=2XY=2X(12-X^2)=24X-2X(的立方）
面积最大将发生在S的一阶导数为0的情况下,所以先求导：
dS/dX=d(24X-2X(的立方）)/dX=24-6X^2=0
再令 24-6X^2=0
则 X^2=24/6=4
所以 X=2
且知最大面积为 S=2XY=2X(12-X^2)=48-16=32平方单位.
再问：最好能画个图。
再答：

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