求函数y=3-4cos(2x+ π/3),x∈[-π/3,π/6]的最大值,最小值及相应的x值

问题描述:

求函数y=3-4cos(2x+ π/3),x∈[-π/3,π/6]的最大值,最小值及相应的x值
1个回答 分类:数学 2014-10-15

问题解答:

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y=3-4cos(2x+ π/3),
∵x∈[-π/3,π/6]
∴2x∈[-2π/3,π/3]
∴2x+ π/3∈[-π/3,2π/3]
当2x+ π/3=0,即x=-π/6时,
cos(2x+ π/3)=-1,y取得最小值-1
当2x+ π/3=2π/3,即x=π/6时,
cos(2x+ π/3)=-1/2,y取得最大值5
 
 
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