1.

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

Answer» `y=sin^3x-6sin^2x+11sinx-6`
Put `sinx=t`
`y=t^3-6t^2+11t-6`
diff. with respect to t
`dy/dt=3t^2-12t+11`
`3(t-2)^2-1>0`
Range[f(-1),f(1)]
Range[-24,0]
`f(-1)=-1-6-11-6=-24`
`f(1)=1-6+11-6=0`.


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