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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingHard2 minQB

MathematicsHardsingle choice

Find all $a$ for which $f (x) = (a + 2) x^{3} - 3 a x^{2} + 9 a x - 1$ is decreasing for every real $x$ .

Options:

Answer:

Solution:

$f I = 3 [(a + 2) x^{2} - 2 a x + 3 a]$ must be nonpositive for all $x$ . Thus $a + 2 < 0$ and the quadratic discriminant is nonpositive: $- 8 a (a + 3) \leq 0$ . Their intersection is $a \leq - 3$ .

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

⏱ 2mℹ️ Source: QB

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