Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingMedium2 minPYQ_2019

MathematicsMediumsingle choice

If $f (x) = x^{3} + b x^{2} + c x + d$ and $0 < b^{2} < c$ , then in $(- \infty, \infty)$

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Answer:

Solution:

$f (x) = x^{3} + b x^{2} + c x + d, 0 < b^{2} < c$ $∴ f^{'} (x) = 3 x^{2} + 2 b x + c$ Discriminant $= 4 b^{2} - 12 c = 4 (b^{2} - 3 c) < 0$ $∴ f^{'} (x) > 0\forall x \in R$ Thus, $f (x)$ is strictly increasing $\forall x \in R$

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

⏱ 2mℹ️ Source: PYQ_2019

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