Question
The interval on which the function $f(x) = 2x^3 + 9x^2 + 12x - 1$ is decreasing is:
✓
Answer
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 $[-2, -1].$
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