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  • Fill in the blanks in each of the If f(x) = |cosx - sinx|, then f’pi/3 ____.

Fill in the blanks in each of the
If f(x) = |cosx - sinx|, then f'\frac{\pi}{3}=____.

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\\ \text { We have, } f(x)=|\cos x-\sin x| \\ \qquad \begin{array}{l} \text { Foc } \frac{\pi}{4}<x<\frac{\pi}{2}, \sin x>\cos x \\ \therefore f(x)=\sin x-\cos x \end{array} \\ \Rightarrow f^{\prime}(x)=\cos x-(-\sin x)=\cos x+\sin x \\ \Rightarrow f^{\prime}\left(\frac{\pi}{3}\right)=\frac{1}{2}+\frac{\sqrt{3}}{2}=\frac{1+\sqrt{3}}{2} \\ \text { Hence, } f^{\prime}\left(\frac{\pi}{3}\right)=\frac{1+\sqrt{3}}{2}

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