Let f(x) = sin^4 x + cos^4 x. Then f is an in | vedclass

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(C) Given $f(x) = \sin^4 x + \cos^4 x$.We know that $\sin^4 x + \cos^4 x = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\sin x \cos

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$\left[ \frac{\pi}{4}, \frac{\pi}{2} \right]$

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(C) Given $f(x) = \sin^4 x + \cos^4 x$.We know that $\sin^4 x + \cos^4 x = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\sin x \cos x)^2 = 1 - \frac{1}{2}\sin^2 2x$.Now,differentiate with respect to $x$:$f'(x) = \frac{d}{dx} (1 - \frac{1}{2}\sin^2 2x) = 0 - \frac{1}{2} \cdot 2\sin 2x \cdot \cos 2x \cdot 2 = -2\sin 2x \cos 2x = -\sin 4x$.For $f(x)$ to be an increasing function,we must have $f'(x) > 0$.So,$-\sin 4x > 0 \implies \sin 4x We know that $\sin 	heta Therefore,$\pi Dividing by $4$,we get $\frac{\pi}{4} Thus,$f(x)$ is an increasing function in the interval $\left[ \frac{\pi}{4}, \frac{\pi}{2} ight]$.

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

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