Q246 / 270 · NDA 2015 (Phase 2) · Mathematics
Consider the function
$f(x)=-2 x^3-9 x^2-12 x+1$
The function $f(x)$ is a decreasing function in the interval
- A$(-2,-1)$
- B$(-\infty,-2)$ only
- C$(-1, \infty)$ only
- Correct answerD$(-\infty,-2) \cup(-1, \infty)$
Solution
For decreasing function $\mathrm{f}^{\prime}(\mathrm{x}) \lt 0$
$\begin{aligned}
& \Rightarrow \quad-\left(6 x^2+18 \mathrm{x}+12\right) \lt 0 \\
& \Rightarrow\left(\mathrm{x}^2+3 \mathrm{x}+2\right) \gt 0 \\
& \Rightarrow(\mathrm{x}+2)(\mathrm{x}+1) \gt 0 \\
& \mathrm{x}=(-\infty,-2) \cup(-1, \infty)
\end{aligned}$
Hence, the correct answer is option: 'D'.