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The value of a for which all extremum of...

The value of a for which all extremum of function `f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1`, lie in the interval (2, 4) is

A

`(3,4)`

B

`(-1,3)`

C

`(-3, -1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=x^(3)-3ax^(2)+3(a^(2)-1)x+1`
`f'(x)=3x^(2)-6ax+3(a^(2)-1)`
`=3(x-(a+1))(x-(a-1))`
so `f'(x)=0 rArr x=a+1 or a-1`
`therefore" "a+1 in (-2, 4)" if " a in (-3,3)`
and `a-1 in (-2,4)" if "a in (-1,5)`
`therefore" "a in (-1,3)`
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