Question

已知函数f(x)=1/2[3ln(x+2)-ln(x-2)]求x为何值时f(x)在[3,7]取得最大值

Answer 1

f(x)=1/2[3ln(x+2)-ln(x-2)] ,x>2

y' =1/2[3/(x+2)-1/(x-2)],y'=0

3/(x+2)=1/(x-2),3x-6=x+2 ,x=4

20

在[3,7]取得最大值=f(7)=1/2ln729/5