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 -

Options

A. `R`
B. `(0,oo)`
C. `(-oo, 0)`
D. `phi`

Answer

D

Explanation

`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`