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....
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/25 21:54:50
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....
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....
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)^2+1]^0.5sin(2x+a) 其中tan a=1/(2X2^0.5)=2^0.5/4
=3sin(2x+a)
0=
y=4√[（2sinxcosx）+2sin(x+π/4)sin(π/4-x)]
=4√[（sin2x）+2sin(x+π/4)cos(x+π/4)]
=4√[（sin2x）+sin(2x+π/2)]
=4√[（sin2x）+(cos2x)]
=4√[√2sin(2x+π/4)]
∵0≤x≤π／2
∴0≤2x≤π...
全部展开
y=4√[（2sinxcosx）+2sin(x+π/4)sin(π/4-x)]
=4√[（sin2x）+2sin(x+π/4)cos(x+π/4)]
=4√[（sin2x）+sin(2x+π/2)]
=4√[（sin2x）+(cos2x)]
=4√[√2sin(2x+π/4)]
∵0≤x≤π／2
∴0≤2x≤π
π/4≤2x+π/4≤5π/4
∴当2x+π/4取π/4和5π/4时，y有最大和最小值
最大值y=4，
当2x+π取5π/4时，根号下的值为负数
∴该函数的最小值为0
y=4√2*（sinxcosx）+2sin(x+π/4)sin(π/4-x)
=2√2(sin2x)+2sin(x+π/4)cos(x+π/4)
=2√2（sin2x）+sin(2x+π/2)
=2√2（sin2x）+cos2x
=3sin(2x+
解不下去了，题目应该搞错了。
收起