MCQ
The values of $ ‘a’$ for which the function $(a + 2){x^3} - 3a{x^2} + 9ax - 1$ decreases monotonically throughout for all real $ x,$ are
- A$a < - 2$
- B$a > - 2$
- C$ - 3 < a < 0$
- ✓$ - \infty < a \le - 3$
then $f'(x) \le 0$ for all $x \in R$
==> $3(a + 2){x^2} - 6ax + 9a \le 0$ for all $x \in R$
==> $(a + 2){x^2} - 2ax + 3a \le 0$ for all $x \in R$
==> $a + 2 < 0$ and Discriminant$ \le 0$
==> $a < - 2$,$ - 8{a^2} - 24a \le 0$ ==> $a < - 2$ and $a(a + 3) \ge 0$
==> $a < - 2$, $a \le - 3$ or $a \ge 0$==> $a \le - 3$==>$ - \infty < a \le - 3$ .
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