Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediuminteger

If the graph of $f (x) = 2 x^{3} + a x^{2} + b x, a, b \in N$ cuts the $x$ -axis at three real and distinct points, then the minimum value of $(a^{2} + b^{2} - 4)$ , is

Answer:

Solution:

$f^{1} (x) = 6 x^{2} + 2 a x + b \Rightarrow 4 a^{2} - 24 b \geq 0$

$\Rightarrow a^{2} \geq 6 b$

$\Rightarrow a \geq 3, b \geq 1, \Rightarrow a = 3, b = 1$

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

⏱ 2mℹ️ Source: QB

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