Question

已知函数y=cos2x-2cosx的值域为[a,b],求4a+（b的平方）的值

Answer 1

y=cos2x-2cosx

=2cos^2 x-2cosx-1

=2(cos^2 x-cosx+1/4)-1-1/2

=2(cosx-1/2)^2-3/2

当cosx=1/2时有最小值y=-3/2

当cosx=-1时有最大值y=3

所以b=3 a=-3/2

4a+b^2

=4*(-3/2)+3^2

=-6+9=3