已知函数f(x)=2根号3sin(x+π/4)cos(x+π/4)+sin2x+a的最大值为1……帮忙丫~
问题描述:
已知函数f(x)=2根号3sin(x+π/4)cos(x+π/4)+sin2x+a的最大值为1……帮忙丫~
已知函数f(x)=2根号3sin(x+π/4)cos(x+π/4)+sin2x+a的最大值为1,
(1)求常数a的值
(2)求函数f(x)的单调增区间
(3)若将f(x)的图像向左平移π/6个单位,得到函数g(x)的图像,求函数g(x)在区间[0,π/2]上最大值和最小值
能做出多少做出多少- -
答
f(x)=2√3sin(x+π/4)cos(x+π/4)+sin2x+a=√3sin(2x+π/2)+sin2x+a=√3cos2x+sin2x+a=2sin(2x+π/3)+a显然:a+2=1 a=-1函数f(x)的单调增区间:2kπ-π/2≤2x+π/3≤2kπ+π/2kπ-5π/12≤x≤kπ+π/12区间为【kπ-5...