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The set of all the possible values of th...

The set of all the possible values of the parameter 'a' so that the function,
`f(x) = x^(3)-3(7-x)x^(2)-3(9-a^(2))x+2`, assume local minimum value at some `x in (-oo, 0)` is -

A

`R`

B

`(0,oo)`

C

`(-oo, 0)`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x) = x^(3) - 3(7-a)x^(2)-3(9-a^(2)) x + 2`
`f'(x) = 3x^(2) - 6(7-a) x - 3 (9-a^(2))`
Since f(x) attains local minimum at some negative x hence both the root of `f'(x)` are rea, distinct and negative
`D gt 0 rArr a lt (58)/(14)"…..(i)`
Sum iof `lt 0 rArr a gt 7 "......."(ii)`
From `(i), (ii)` and `(iii)` , we get `a in phi`
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Knowledge Check

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    `-9`
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    16

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