Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minPYQ_2018

MathematicsEasysingle choice

For which interval the given function $f (x) = - 2 x^{3} - 9 x^{2} - 12 x + 1$ is decreasing?

Answer:

Solution:

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

$f^{'} (x) = - 6 x^{2} - 18 x - 12$

To be decreasing $f^{'} (x) < 0$

$\Rightarrow - 6 x^{2} - 18 x - 12 < 0$

$\Rightarrow x^{2} + 3 x + 2 > 0$

$\Rightarrow (x + 2) (x + 1) > 0$

Therefore, either $x < - 2$ or $x > - 1$

$x \in (- 1, \infty)$ or $(- \infty, - 2)$

Hence, option (d) correct.

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: PYQ_2018

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