Question

求使下列函数取得最大值、最小值的自变量X的集合,并分别写出最大值、最小值是什么

Answer 1

(1)Y=-5sinx,x∈R -1≤Y=sinx≤1,且当x=π/2+2kπ时Y=sinx=1、x=3π/2+2kπ时Y=sinx=-1 故-5≤Y=-5sinx≤5,当x=3π/2+2kπ时Y=sinx=-1,Y=-5sinx=5 当x=π/2+2kπ时Y=sinx=1,Y=-5sinx=-5 (2)Y=1-12cosx,x∈R -1≤Y=cosx≤1,且当x=2kπ时Y=cosx=1、x=π+2kπ时Y=cosx=-1 故3/2≤Y=1-12cosx≤1/2,当x=π+2kπ时Y=cosx=-1,Y=1-12cosx=3/2 当x=2kπ时Y=cosx=1,Y=1-12cosx=-3/2(3)y=3sin(2x+π3),x∈R -1≤y=3sin(2x+π3)≤1,且当2x+π3=π/2+2kπ时y=sinx=1、2x+π3=3π/2+2kπ时Y=sinx=-1 故-3≤y=3sin(2x+π3)≤3,当x=π/12+2kπ时y=3sin(2x+π3)=3 当x=7π/12+2kπ时y=3sin(2x+π3)=-3(4)y=12sin(12x+14π),x∈R没分清楚是1（2x）+1（4π）还是12×x+14×π用同样的方法求出即可