The interval on which the function f ( x ) = 2 x 3 + 9 x 2 + 12 x - 1 is decreasing is:

Question

The interval on which the function $f (x) = 2 x^{3} + 9 x^{2} + 12 x - 1$ is decreasing is:

Smart Achievers · Accepted Answer

(2)

Ans. $[- 2, - 1]$

Explanation:

We have, $f (x) = 2 x^{3} + 9 x^{2} + 12 x - 1$

$∴$ $f' (x) = 6 x^{2} + 18 x + 12$

$= 6 (x^{2} + 3 x + 2) = 6 (x + 2) (x + 1)$

So, $f' (x) \leq 0,$ for decreasing.

On drawing the number line as below:

We see that $f' (x)$ is decreasing in $[- 2, - 1] .$

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