求函数y=2cos(x-π/3)(π/6≤x≤2π/3)最大值

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求函数y=2cos(x-π/3)(π/6≤x≤2π/3)最大值

求函数y=2cos(x-π/3)(π/6≤x≤2π/3)最大值
求函数y=2cos(x-π/3)(π/6≤x≤2π/3)最大值

求函数y=2cos(x-π/3)(π/6≤x≤2π/3)最大值
π/6≤x≤2π/3
-π/6≤x-π/3≤π/3
余弦函数的图像,可得,在0处最大值为1 :cos(x-π/3)在cos(π/3-π/3)=1
最大值为 2×1=2

π/6≤x≤2π/3
-π/6≤x-π/3π≤π/3
cos(x-π/3)在[-π/6,0]单调增,在(0,π/3]单调减
当x=π/3时有最大值,最大值=2

画个图像不就出来了