设函数f(x)=4cos²wx-4√3sinwx*coswx+b的最小正周期为π(w>0)(1)求w的值 (2)若f(x)的定义域为【-π/3,π/6】,值域是【-1,5】,求b的值及f(x)的单调减区间
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![设函数f(x)=4cos²wx-4√3sinwx*coswx+b的最小正周期为π(w>0)(1)求w的值 (2)若f(x)的定义域为【-π/3,π/6】,值域是【-1,5】,求b的值及f(x)的单调减区间](/uploads/image/z/981800-8-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D4cos%26%23178%3Bwx-4%E2%88%9A3sinwx%2Acoswx%2Bb%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E4%B8%BA%CF%80%EF%BC%88w%EF%BC%9E0%EF%BC%89%281%29%E6%B1%82w%E7%9A%84%E5%80%BC+%282%29%E8%8B%A5f%28x%29%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%E3%80%90-%CF%80%2F3%2C%CF%80%2F6%E3%80%91%2C%E5%80%BC%E5%9F%9F%E6%98%AF%E3%80%90-1%2C5%E3%80%91%2C%E6%B1%82b%E7%9A%84%E5%80%BC%E5%8F%8Af%EF%BC%88x%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%87%8F%E5%8C%BA%E9%97%B4)
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设函数f(x)=4cos²wx-4√3sinwx*coswx+b的最小正周期为π(w>0)(1)求w的值 (2)若f(x)的定义域为【-π/3,π/6】,值域是【-1,5】,求b的值及f(x)的单调减区间
设函数f(x)=4cos²wx-4√3sinwx*coswx+b的最小正周期为π(w>0)
(1)求w的值 (2)若f(x)的定义域为【-π/3,π/6】,值域是【-1,5】,求b的值及f(x)的单调减区间
设函数f(x)=4cos²wx-4√3sinwx*coswx+b的最小正周期为π(w>0)(1)求w的值 (2)若f(x)的定义域为【-π/3,π/6】,值域是【-1,5】,求b的值及f(x)的单调减区间
f(x)=4cos²wx-4√3sinwx*coswx+b
=2(cos2wx+1)-2√3sin2wx+b
=2cos2wx-2√3sin2wx+b+2
=4cos(2wx+π/3 )+b+2
(1)最小正周期T=2π/(2w)=π
所以w=1
则f(x)=4cos(2x+π/3 )+b+2
(2)因-π/3≤x≤π/6
所以-π/3≤2x+π/3≤2π/3
-2≤4cos(2wx+π/3 )≤4
b≤4cos(2wx+π/3 )+b+2≤b+6
又值域是【-1,5】,
所以b=-1
则f(x)=4cos(2x+π/3 )+1
的单调减区间是2kπ≤2x+π/3≤2kπ+π
即kπ-π/6≤x≤kπ+π/3(k为整数)