The values of ‘a’ for which the function $(a+2)x^3-3ax^2+9ax-1$ decreases monotonically throughout for all real x are:
Answer & explanation
Correct answer: option 4
$f(x)=(a+2)x^3-3ax^2+9ax-1⇒f'(x)=3(a+2)x^2-6ax+9a<0\,∀\,x∈R$
$⇒a+2<0,36a^2-4.3(a+2)9a<0⇒a<-2,a^2-3a(a+2)<0$ $a<-2,-2a^2-6a<0$
$⇒a<-2,a<-3,a>0⇒a∈(-∞,-3)$