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函数f(x)的解析式是y=2sin(π/4x+π/4)

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/14 04:30:58
函数f(x)的解析式是y=2sin(π/4x+π/4)
当X属于-6到-2/3时,求函数y=f(x)+f(x+2)的最大值和最小值,及相应的x的取值
y=f(x)+f(x+2)
=2sin(π/4x+π/4)+2sin[π/4(x+2)+π/4]
=2sin(π/4x+π/4)+2sin(π/4 x+3π/4)
=2sin(π/4x+π/4)+2sin(π/4-π/4x)
展开,化简得
=2√2cos(π/4 x)
∵ -6≤x≤-2/3
∴ -3π/2≤π/4 x≤-π/6
∴ π/4 x=-π/6,即x=-2/3时,f(x)有最大值2√2*(√3/2)=√6
π/4 x=-π,即x=-4时,f(x)有最小值2√2*(-1)=-2√2
再问: 张开后变成 2sinπ/4xcosπ/4+2cosπ/4xsinπ/4+2sinπ/4xcos3π/4+2cosπ/4xsin3π/4 然后怎么变成=2√2cos(π/4 x)啊
再答: 2sinπ/4xcosπ/4+2cosπ/4xsinπ/4+2sinπ/4xcos3π/4+2cosπ/4xsin3π/4 =√2sinπ/4x+√2cosπ/4x-√2sinπ/4x+√2cosπ/4x =2√2cos(π/4 x)