已知函数f(x)=sinxcosx+sin^2x.

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.

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.