已知0≤x≤π/2,函数y=4倍根号下2×正弦x×余弦x+2倍正弦(x+π/4)×正弦(π/4-x)的极值?

问题描述:

已知0≤x≤π/2,函数y=4倍根号下2×正弦x×余弦x+2倍正弦(x+π/4)×正弦(π/4-x)的极值?
y=(4倍根号2)乘以(正弦x×余弦x)加....

y=4X2^0.5Xsinxcosx+2Xsin(x+π/4)sin(π/4-x)=2X2^0.5sin(2x)+2Xsin(x+π/4)sin[π/2-(π/4+x)]=2X2^0.5sin(2x)+2Xsin(x+π/4)cos(π/4+x)=2X2^0.5sin(2x)+sin(2x+π/2)=2X2^0.5sin(2x)+cos(2x)=[(2X2^0.5)...