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Separate the intervals of monotonocity f...

Separate the intervals of monotonocity for the function `f(x)=-2x^3-9x^2-12 x+1`

A

`(-2,-1)`

B

`(-oo,-2)`

C

`(-1,2)`

D

`(-1,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=-2x^(3)-9x^(2)-12x+1`
`f'(x)=-6x^(2)-18x-12`
for increasing function `f(x)gt0`
`rarr -(6x^(2)+18x+12)+1`
`rarr (x^(2)+3x+2)lt0`
`rarr (x+2)(x+1)lt0`
`x=(-2,-1)`
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