The function f(x) is a decreasing funciton in the interval

Options

A. `(-2,-1)`
B. `(-oo,-2)`
C. `(-1,2)`
D. `(-oo,-2)` `cup` `(-1,oo)`

Answer

D

Explanation

For decreasing function `f(x) lt0`
`rarr -(6x^(2)+18x+12)lt0`
`rarr (x^(2)+3x+2)gt0`
`rarr (x+2)(x+1)gt0`
`x=(-oo,-2)cup(-1,oo)`
`f(theta) = 4sin^(2) theta +cos^(4) theta)`
`=4 (sin^(2) theta +cos^(2) theta(1-sin^(2) theta)`
`=(1-1/4sin^(2) 2theta)`