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If f(x)=3x^(4)+4x^(3)-12x^(2)+12, then f...

If `f(x)=3x^(4)+4x^(3)-12x^(2)+12`, then f(x) is

A

increasing in `(-oo,2) and ` in (0,1)

B

increasing in (-2,0) and in `(1,oo)`

C

decreasing in `(-2,0) and `in (0,1)

D

decreasing in `(-oo,-2) and `in (1,`oo`)

Text Solution

Verified by Experts

The correct Answer is:
B
Since,
`f(x)=3x^(4)+4x^(3)-12x^(2)+12`
`f'(x)=12x^(3)+12x^(2)-24x`
`=12x(x-1)(x+2)`
For above, it is clear that `f'(x)` is increasing in `(-2,0) and in `(1,oo)`
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