求函数y=2cos(x-π/3)(π/6≤x≤2π/3)的最大值最小值,并写出对应的x的值

题目

求函数y=2cos(x-π/3)(π/6≤x≤2π/3)的最大值最小值,并写出对应的x的值

答案

y=2cos(x-π/3)(π/6≤x≤2π/3)
令t= x-π/3,y=2cost.
∵π/6≤x≤2π/3,∴-π/6≤x-π/3≤π/3,
-π/6≤t≤π/3.
函数y=2cost在t=π/3（即x=2π/3）时,取到最小值1.
在t=0（即x=π/3）时,取到最小值2.