MCQ
Choose the correct answer from the given four options: The interval on which the function $f(x)=2 x^3+9 x^2+12 x-1$ is decreasing is$:\ \quad$
- A$[-1,\infty)$
- ✓$[-2,-1]$
- C$(-\infty ,-2]$
- D$[-1,1]$
✓
Answer
Correct option: B.
$[-2,-1]$
We have, $f(x)=2 x^3+9 x^2+12 x-1$
$\therefore f^{\prime}(x)=6 x^2+18 x+12$
$=6\left(x^2+3 x+2\right)=6(x+2)(x+1)$
So, $\text{f}\ '(\text{x})\leq0,$ for decreasing.
On drawing number lines as below.
We see that $f\ '(x)$ is decreasing in $[-2, -1].$
$\therefore f^{\prime}(x)=6 x^2+18 x+12$
$=6\left(x^2+3 x+2\right)=6(x+2)(x+1)$
So, $\text{f}\ '(\text{x})\leq0,$ for decreasing.
On drawing number lines as below.
We see that $f\ '(x)$ is decreasing in $[-2, -1].$
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