The function f(x) = sin^4 x + cos^4 x increas | vedclass

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(B) Given the function $f(x) = \sin^4 x + \cos^4 x$. We can rewrite this as $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\s

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$\frac{\pi}{4} < x < \frac{\pi}{2}$

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(B) Given the function $f(x) = \sin^4 x + \cos^4 x$. We can rewrite this as $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\sin x \cos x)^2 = 1 - \frac{1}{2}\sin^2(2x)$. To find where the function increases,we find the derivative $f'(x) = -\frac{1}{2} \cdot 2\sin(2x) \cdot \cos(2x) \cdot 2 = -\sin(4x)$. The function increases when $f'(x) > 0$,which means $-\sin(4x) > 0$,or $\sin(4x) This occurs when $\pi < 4x < 2\pi$,which simplifies to $\frac{\pi}{4} < x < \frac{\pi}{2}$.

The function $f(x) = \sin^4 x + \cos^4 x$ increases if

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