Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minPYQ_2008

MathematicsMediumsingle choice

Suppose the cube $x^{3} - p x + q$ has three distinct real roots where $p > 0$ and $q > 0$ . Then which one of the following holds?

Answer:

Solution:

Let $f (x) = x^{3} - p x + q$ Now for maxima/minima $f^{'} (x) = 0 \Rightarrow 3 x^{2} - p = 0 \Rightarrow x^{2} = \frac{p}{3} ∴ x = \pm \frac{p}{3}$

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

⏱ 2mℹ️ Source: PYQ_2008

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