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24. Find the intervals in which the foll...

24. Find the intervals in which the following function is (a) increasing and (b) decreasing `f(x)=2x^3+9x^2+12x-1`

A

`[-1,infty]`

B

`[-2,-1]`

C

`(-infty,-2)`

D

`[-1,1]`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, f(x)=`2x^(3)+9x^(2)+12x-1`
`therefore f^(')(x) = 6x^(2)+18x+12`
`=6(x^(2)+3x+2)=6(x+2)(x+1)`
So, `f^(')(x)le0`, for decreasing.
On drawing number lines as below

We see that `f^(')(x)`is decreasing in `[-2,-1]`.
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