What is themaximum value of 16 `sin theta -12 sin^(2) theta`?

Options

A. `3/4`
B. `4/3`
C. `16/3`
D. 4

Answer

C

Explanation

`f(theta)=16 sin theta -12 sin^(2) theta`
`f'(theta)=16 cos theta -24 sin theta cos thetaa`
`f'(theta) =0 rarr cos theta (16(16-24 sin theta) =0`
`rarr cos theta =0 (or ) 16-24 sin theta =0`
`f((pi)/(2))=16 sin (pi)/(2)-12sin^(2)(pi)/(2)=16-12=4`
`f(sin^(theta)=2/3)=16(2/3)-12(2/3)^(2)`
`=32/3-(48)/(9)=32/3-16/3=16/3`