己知函数f(x)=√3sinxcosx+cos^2x-1/2.(1)求f(x)的单调区间(2)求f(x)在区间[-(5/12)¶,(1/24)¶]上的最大值和最小值

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 22:53:59
己知函数f(x)=√3sinxcosx+cos^2x-1/2.(1)求f(x)的单调区间(2)求f(x)在区间[-(5/12)¶,(1/24)¶]上的最大值和最小值

己知函数f(x)=√3sinxcosx+cos^2x-1/2.(1)求f(x)的单调区间(2)求f(x)在区间[-(5/12)¶,(1/24)¶]上的最大值和最小值
己知函数f(x)=√3sinxcosx+cos^2x-1/2.(1)求f(x)的单调区间(2)求f(x)在区间[-(5/12)¶,(1/24)¶]上的最大值和最小值

己知函数f(x)=√3sinxcosx+cos^2x-1/2.(1)求f(x)的单调区间(2)求f(x)在区间[-(5/12)¶,(1/24)¶]上的最大值和最小值
f(x)=√3sinxcosx+cos^2x-1/2
=√3/2sin2x+1/2cos2x
=sin(2x+π/6)
1) 2kπ-π/2≤2x+π/6≤2kπ+π/2
kπ-π/3≤x≤kπ+π/6
单增区间:[kπ-π/3,kπ+π/6(k∈Z)]
单减区间:[kπ+π/6,kπ+2π/3(k∈Z)]
2) -π/3∈[-5π/12,π/24]
ymin=f(-π/3)=-1
ymax=f(π/24)=√2/2