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数学
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a=(sin(2x+π/6)+1/2,m),b=(1,-m),且f(x)=ab
(其中ab表示向量)
(1)求函数f(x)的解析式
(2)当x∈[-π/6,π/3]时,f(x)的最小值是-4,求此时函数f(x)的最大值,并求出相应的x的值
人气:139 ℃ 时间:2020-04-03 14:00:25
解答
(1) f(x)=ab=sin(2x+π/6)+1/2-m²
(2) f(x)是周期为π的周期函数,当x∈[-π/6,π/3]时
f(x)在[-π/6,π/6]单调递增,在[π/6,π/3]单调递减
f(x)最小值在x=-π/6处取到
∴f(-π/6)=sin(-π/6)+1/2-m²=-4
即m²=4
f(x)=sin(2x+π/6)-7/2
f(x)最大值在x=π/6处取到,此时
f(π/6)=sin(π/2)-7/2=-5/2
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