求函数y=2cos﹙x-π/3﹚﹙π/6≤x≤2π/3﹚的最大值和最小值

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求函数y=2cos﹙x-π/3﹚﹙π/6≤x≤2π/3﹚的最大值和最小值
求函数y=2cos﹙x-π/3﹚﹙π/6≤x≤2π/3﹚的最大值和最小值

求函数y=2cos﹙x-π/3﹚﹙π/6≤x≤2π/3﹚的最大值和最小值
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.

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.