If x is real, the maximum value of 3 x 2 + 9 x + 7 3 x 2 + 9 x + 17 is

y = 3 x 2 + 9 x + 7 3 x 2 + 9 x + 17 3 x 2 ( y − 1 ) + 9 x ( y − 1 ) + 7 y − 17 = 0 D ≥ 0 ∵ x is real 81 ( y − 1 ) 2 − 4 x 3 ( y − 1 ) ( 7 y − 17 ) ≥ 0 ⇒ ( y − 1 ) ( y − 41 ) ≤ 0 ⇒ 1 ≤ y ≤ 41

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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaHard2 minPYQ_2006

MathematicsHardsingle choice

If $x$ is real, the maximum value of $\frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ is

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Solution:

$y = \frac{3 x ^{2} + 9 x + 17}{3 x ^{2} + 9 x + 7}$ $3 x^{2} (y - 1) + 9 x (y - 1) + 7 y - 17 = 0$ $D \geq 0 ∵ x$ is real $81 (y - 1)^{2} - 4 x 3 (y - 1) (7 y - 17) \geq 0$ $\Rightarrow (y - 1) (y - 41) \leq 0 \Rightarrow 1 \leq y \leq 41$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: PYQ_2006

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