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