If the function ` f(x) = x^3 + 3(1-7)x^2 +3(a^2-9)x-1 ` has a positive point Maximum , then

Options

A. `ain(3,oo)cup(-oo,-3)`
B. `ain(-oo,-3)cup(3,29//7)`
C. `(-oo,7)`
D. `(-oo,29//7)`

Answer

2

Explanation

`f(x)=3x^(2)+6(a-7)x+3(a^(2)-9)=0`
`rArrx^(2)+2(a-7)x+3(a^(2)-9)=0`
`rArr(-2(a-7)pmsqrt(4(a-7)^(2)-4(a^(2)-9)))/(2)`
`=-(a-7)pmsqrt(58-14a)`
For positive maximum

(i)`a+betagt0` , (ii)`abetagt0`, (iii) `Dgt0`
(i) `-(a-7)gt0`
`rArralt7`
(ii) `a^(2)-9gt0`
`rArr ain(-oo,-3)cup(3,oo)`
(iii) `58-149gt0`
`rArralt(29)/(7)`
From(1),(2) and (3)
`in(-oo,-3)cup(3,(29)/(7))`