Find the range of `y=sin^3x-6sin^2x+11sinx-6.`

Options

A. `[-24, 2]`
B. `[-24,0]`
C. `[0,24]`
D. `[-24,24]`

Answer

B

Explanation

`y=sin^(3)x-6sin^(2)x+11 sin x-6`
Put sin x = 1
`therefore y=t^(3)-6t^(2)+11t-6,-1le t le 1`
`therefore (dy)/(dt)=3t^(2)-12t+11=3(t-2)^(2)-1gt 0` for `-1le t le 1`
`therefore` Function is increasing
Hence, range is `[f(-1),f(1)]` or `[-24,0]`