Question

Let $f\left(x\right)=x^3+6x^2+px+2.$ If the largest possible interval in which f(x) is a decreasing function in $(-3,-1)$ then $p$ is equal to:

• A. $2$
• B. $6$
• C. $8$
• D. $9$

Answer 1

The correct option is D $9$

$f^{\prime }\left(x\right)=3x^2+12x+p=-ive(-3,-1)$
$\therefore f^{\prime }\left(x\right)=\lambda (x+3)(x+1)=\lambda (x^2-4x+3)$
Comparing $\lambda =3andp=3\lambda =9$