设f(x)=(cosx+sinx)sinx,且x∈{0,π/2},则函数f(x)的最大值

问题描述:

设f(x)=(cosx+sinx)sinx,且x∈{0,π/2},则函数f(x)的最大值

f(x)=(cosx+sinx)sinx=sinxcosx+sinx^2=1/2*sin2x+1/2(1-cos2x)
=1/2*(sin2x-cos2x)+1/2
=√2/2*sin(2x-π/4)+1/2