A total of x feet of fencing is to form three sides of a level rectangular yard. What is the(继续) maximum possible area o
问题描述：
A total of x feet of fencing is to form three sides of a level rectangular yard. What is the(继续) maximum possible area of the yard, in terms of x?
(A)x^2/9(B)x^2/8(C)x^2/4(D)x^2(E)2x^2
选B.怎么做?谢谢!
答
设中间那个边为a,两边为b
有a+2b=x,x是常数,a=x-2b
有S=ab,即S=（x-2b）b=-2(b^2-0.5xb+(0.25x)^2)+(0.25x)^2既化为那种一个二次项的形式
所以S的最大值选B（x-2b）b=-2(b^2-0.5xb+(0.25x)^2)+(0.25x)^2是怎么来的？0.5,0,25是怎么来的?S=(x-2b)*b=Xb-2b^2,提-2 有S=-2[b^2-(x/2)*b]，然后括号内配方， 根据完全平方公式m^2+-2mn+n^2=(m-n)^2 可以看出在这个式子里有m=b 2mn=(x/2)b 所以推出n=x/4 即原式为S=-2[b-(x/4)]^2+2*(x/4)^2,这样这个式子仍和原式相等，因为在括号内减去的（括号系数是负的）又在括号外加回来了。 所以S的最大值取在括号内为0时，为（x^2)/8