Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingEasy2 minQB

MathematicsEasysingle choice

Let $f : (0, \infty) \to R$ be a (strictly) decreasing function. If

$f (2 a^{2} + a + 1) < f (3 a^{2} - 4 a + 1)$ , then the range of $a \in R$ is

Options:

Answer:

Solution:

we have $2 a^{2} + a + 1 > 3 a^{2} - 4 a + 1 \Rightarrow a^{2} - 5 a < 0 \Rightarrow 0 < a < 5$ $ALSO 3 a^{2} - 4 a + 1 > (3 a - 1) (a - 1) > 0 \Rightarrow a \in (- \infty, 1/3) \cup (1, \infty)$

INTERSECTION OF (A) AND (B) YIELDS $a \in (0, 1/3) \cup (1, 5)$

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

⏱ 2mℹ️ Source: QB

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