The interval in which the function f ( x ) = x 4 x 2 + 1 is decreasing is :

Given f ( x ) = x 4 x 2 + 1 Thus f ′ ( x ) = 4 − x 2 1 f ( x ) will be decreasing if f ′ ( x ) 4 ⇒ 2 − 1 < x < 2 1 Thus interval in which f ( x ) is decreasing, is ( − 2 1 , 2 1 )

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MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minPYQ_2018

MathematicsEasysingle choice

The interval in which the function $f (x) = \frac{4 x ^{2} + 1}{x}$ is decreasing is :

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Solution:

Given $f (x) = \frac{4 x ^{2} + 1}{x}$ Thus $f^{'} (x) = 4 - \frac{1}{x ^{2}}$ $f (x)$ will be decreasing if $f^{'} (x) < 0$ Thus $4 - \frac{1}{x ^{2}} < 0$ $\Rightarrow \frac{1}{x ^{2}} > 4 \Rightarrow \frac{- 1}{2} < x < \frac{1}{2}$ Thus interval in which $f (x)$ is decreasing, is $(- \frac{1}{2}, \frac{1}{2})$

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

⏱ 2mℹ️ Source: PYQ_2018

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