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
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 21:06:13
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
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
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
y=2sin(π/4x+π/4)+2sin[π/4(x+2)+π/4]
=2sin(π/4x+π/4)+2sin(π/4x+3π/4)
= 2sinπ/4x*根号2/2+2cosπ/4x*根号2/2+2sinπ/4x*(-根号2/2)+2cosπ/4x*根号2/2
=2根号2cosπ/4x
∵ X属于-6到-2/3∴-...
全部展开
y=2sin(π/4x+π/4)+2sin[π/4(x+2)+π/4]
=2sin(π/4x+π/4)+2sin(π/4x+3π/4)
= 2sinπ/4x*根号2/2+2cosπ/4x*根号2/2+2sinπ/4x*(-根号2/2)+2cosπ/4x*根号2/2
=2根号2cosπ/4x
∵ X属于-6到-2/3∴-3 π/2<π/4x<-π/6
∴当π/4x=-π/6时,即x=-2/3时, 最大值2根号2cos(-π/6)=2根号2*根号3/2=根号6
当π/4x=-π时,即x=-4时, 最小值2根号2cos(-π)=2根号2*(-1)=-2根号2
收起