Question

函数f(x)=cos2x-cosx+1在[π/3,5π/6]上的值域

Answer 1

f(x)=cos2x-cosx+1

=2cos²x-1-cosx+1

=2cos²x-cosx

看成二次函数,其对称轴=1/4

cosπ/3=1/2

cos5π/6=-√3/2

所以cosx能取到对称轴

f(x)min=2*1/16-1/4=-1/8

f(x)max=2*(-√3/2)^2+√3/2=(3+√3)/2

值域[-1/8,(3+√3)/2]