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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaHard2 minPYQ_2016

MathematicsHardsingle choice

Let $f (x) = \sin^{4} x + \cos^{4} x .$ Then, $f$ is an increasing function in the interval:

Question diagram: Let f x = sin 4 ⁡ x + cos 4 ⁡ x . Then, f is an increasing f

Options:

Answer:

Solution:

$f (x) = \sin^{4} x + \cos^{4} x$

$f^{'} (x) = 4 \sin^{3} x \cos x + 4 \cos^{3} x (- \sin x)$

$= 4 \sin x \cos x (\sin^{2} x - \cos^{2} x)$

$= - 2 \sin 2 x \cos 2 x$

$= - \sin 4 x$

$f (x)$ , is increasing when $f^{'} (x) > 0$

$\Rightarrow$ $- \sin 4 x > 0$

$\Rightarrow$ $\sin 4 x < 0$

$\Rightarrow π < 4 x < 2 π$

$\Rightarrow \frac{π}{4} < x < \frac{π}{2}$
$\Rightarrow$ $x \in (\frac{π}{4}, \frac{π}{2})$

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

⏱ 2mℹ️ Source: PYQ_2016

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