Let f x = 3 sin 4 x + 10 sin 3 x + 6 sin 2 x - 3 , x ∈ - π 6 , π 2 . Then, f is :

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MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minPYQ_2021

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Let $f (x) = 3 \sin^{4} x + 10 \sin^{3} x + 6 \sin^{2} x - 3$ , $x \in [- \frac{π}{6}, \frac{π}{2}]$ . Then, $f$ is :

Answer:

Solution:

$f (x) = 3 \sin^{4} x + 10 \sin^{3} x + 6 \sin^{2} x - 3, x \in [- \frac{π}{6}, \frac{π}{2}]$

$\Rightarrow f^{'} (x) = 12 \sin^{3} x \cos x + 30 \sin^{2} x \cos x + 12 \sin x \cos x$

$= 6 \sin x \cos x (2 \sin^{2} x + 5 \sin x + 2)$

$= 6 \sin x \cos x (2 \sin x + 1) (\sin x + 2)$

From wavy curve, we can say $f' (x) < 0$ in $(- \frac{π}{6}, 0)$

So, the function is Decreasing in $(- \frac{π}{6}, 0)$

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

⏱ 2mℹ️ Source: PYQ_2021

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