If f(x)=|cos x-sin x| , then f^′ ((Π)/6 ) is equal to

Correct answer: (A) -1/2(1+√3). Given that, f(x)=|cos x-sin x| So, f^′(x)=-sin x-cos x At x=(Π)/6 , we have f^′ ((Π)/6 )=-sin ((Π)/6 )-cos ((Π)/6 ) =-1/2-(√3)/2=(-1)/2(1+√3)

Q110 / 180 · KCET 2018 · Mathematics

If $ f(x)=|\cos x-\sin x| $, then $ f^{\prime}\left(\frac{\Pi}{6}\right) $ is equal to

Correct answer
A
$ -\frac{1}{2}(1+\sqrt{3}) $
B
$ \frac{1}{2}(1+\sqrt{3}) $
C
$ -\frac{1}{2}(1-\sqrt{3}) $
D
$ \frac{1}{2}(1-\sqrt{3}) $

Solution

Given that, $f(x)=|\cos x-\sin x|$ So, $f^{\prime}(x)=-\sin x-\cos x$ At $x=\frac{\Pi}{6}$, we have $f^{\prime}\left(\frac{\Pi}{6}\right)=-\sin \left(\frac{\Pi}{6}\right)-\cos \left(\frac{\Pi}{6}\right)$ $=-\frac{1}{2}-\frac{\sqrt{3}}{2}=\frac{-1}{2}(1+\sqrt{3})$

Hence, the correct answer is option: 'A'.

If \( f(x)=|\cos x-\sin x| \), then \( f^{\prime}\left(\frac{\Pi}{6}\right) \) is equal to

Solution

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