Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minPYQ_2012

MathematicsEasysingle choice

If $f (x) = \frac{a ^{2} - 1}{a ^{2} + 1} x^{3} - 3 x + 5$ is a decreasing function of $x$ in $R$ , then the set of possible values of a (independent of $x$ ) is

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Answer:

Solution:

$f^{'} (x) = 3 (\frac{a ^{2} - 1}{a ^{2} + 1}) x^{2} - 3$ $f^{'} (x) < 0$ for all $x$ if $a^{2} - 1 \leq 0 \Rightarrow - 1 \leq a \leq 1$

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

⏱ 2mℹ️ Source: PYQ_2012

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