If f(x) = sin x - cos x, the function is decr | vedclass

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(D) Given $f(x) = \sin x - \cos x.$First,find the derivative $f'(x)$:$f'(x) = \cos x + \sin x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos x + \frac{1}{\

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None of these

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(D) Given $f(x) = \sin x - \cos x.$First,find the derivative $f'(x)$:$f'(x) = \cos x + \sin x = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos x + \frac{1}{\sqrt{2}} \sin x ight) = \sqrt{2} \sin(x + \pi/4).$For the function to be decreasing,we require $f'(x) $\sqrt{2} \sin(x + \pi/4) $\sin(x + \pi/4) In the interval $0 \le x \le 2\pi$,the argument $	heta = x + \pi/4$ ranges from $\pi/4$ to $9\pi/4$.The sine function is negative in the interval $(\pi, 2\pi)$.Therefore,$\pi Subtracting $\pi/4$ from all sides:$3\pi/4 Comparing this with the given options,none of the intervals provided are subsets of $(3\pi/4, 7\pi/4)$.Thus,the correct option is $(d)$.

If $f(x) = \sin x - \cos x,$ the function is decreasing in the interval $0 \le x \le 2\pi$ for which of the following?

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