Q245 / 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 an increasing function in the interval
- Correct answerA$(-2,-1)$
- B$(-\infty,-2)$
- C$(-1,2)$
- D$(-1, \infty)$
Solution
$\begin{aligned}
& f(x)=-2 x^3-9 x^2-12 x+1 \\
& f^{\prime}(x)=-6 x^2-18 x-12
\end{aligned}$
for increasing function $\mathrm{f}^{\prime}(\mathrm{x}) \gt 0$
$\begin{aligned}
& \Rightarrow \quad-\left(6 x^2+18 x+12\right) \gt 0 \\
& \Rightarrow \quad\left(x^2+3 x+2\right) \lt 0 \\
& \Rightarrow \quad(x+2)(x+1) \lt 0 \\
& x=(-2,-1)
\end{aligned}$
Hence, the correct answer is option: 'A'.