已知函数f(x)=sinxcosx+sin^2x.(1)求f(π/4)的值
问题描述：
已知函数f(x)=sinxcosx+sin^2x.(1)求f(π/4)的值
(2)若x包含于[0,π/2],求f(x)的最大值和相应的x的值
答
f(x) = sinxcosx+sin²x = 0.5*sin2x + 0.5*(1-cos2x) = 0.5*(1 + sin2x - cos2x)
f(π/4) = 0.5*(1 + 1 - 0) = 1
进一步化简f(x)
f(x) = 0.5*(1 + sin2x - cos2x) = 0.5 + 0.5*√2 *sin(2x - π/4)
x属于0到π/2,所以2x属于0到π
当2x - π/4等于π/2时,即x = 3π/8时 f(x)最大
f(3π/8) = 0.5+0.5*√2