已知函数f(x)=sinxcosx+sin^2x.1.求f(π/4)的值.2.若x属于[0,π/2],求f(x)的最大值及相应的x值.
问题描述：
已知函数f(x)=sinxcosx+sin^2x.
1.求f(π/4)的值.2.若x属于[0,π/2],求f(x)的最大值及相应的x值.
答
(1)解析：f(x)=sinxcosx+sin^2x=1/2sin2x-1/2cos2x+1/2=√2/2sin(2x-π/4)+1/2
f(π/4)=1
(2)解析：∵x属于[0,π/2]
2x-π/4=π/2==>x=3π/8,∴函数f(x)在x=3π/8处取极大值F(3π/8)=(√2+1)/2
答
这么简单的题目都不会？好好看书吧！
答
f(x)=(1/2)sin2x－(1/2)cos2x＋(1/2)=(√2/2)sin(2x－π/4)＋(1/2).1、代入计算,f(π/4)=1/2；2、x在[0,π/2],则2x－π/4在[－π/4,3π/4],最大是f(3π/8)=√2/2＋1/2,最小是f(0)=0.