已知函数f(x)=2sin2x+2又根号3 cos2x+1 (1)求f(π/3)的值 (2)求f(x)的最大值和最小...
问题描述:
已知函数f(x)=2sin2x+2又根号3 cos2x+1 (1)求f(π/3)的值 (2)求f(x)的最大值和最小...
已知函数f(x)=2sin2x+2又根号3 cos2x+1
(1)求f(π/3)的值
(2)求f(x)的最大值和最小值及相应的x值
(3)求函数f(x)的单调递增区间
答
f(x)=2sin2x+2√3 cos2x+1=4(1/2sin2x+√3/2cos2x)+1=4sin(2x+π/3)+1(1)f(π/3)=4sin(2π/3+π/3)+1=1(2)当2x+π/3=2kπ+π/2即x=kπ+π/12时,f(x)取得最大值5当2x+π/3=2kπ-π/2即x=kπ-5...