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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaHard2 minPYQ_2008

MathematicsHardsingle choice

How many real solutions does the equation $x^{7} + 14 x^{5} + 16 x^{3} + 30 x - 560 = 0$ have?

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Answer:

Solution:

$x^{7} + 14 x^{5} + 16 x^{3} + 30 x - 560 = 0 Let f (x) = x^{7} + 14 x^{5} + 16 x^{3} + 30 x \Rightarrow f^{'} (x) = 7 x^{6} + 70 x^{4} + 48 x^{2} + 30 > 0\forall x$ $∴ f (x)$ is an increasing function $\forall x$ .

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

⏱ 2mℹ️ Source: PYQ_2008

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