Question

If $f\left(x\right)=\left|\cos 2x\right|$ then $f^{{}^{\prime }}\left(\frac{\pi }{4}+0\right)$ is equal to

• A. $2$
• B. $0$
• C. $-2$
• D. $noneofthese$

Answer 1

The correct option is A $2$

$f\left(x\right)=\left|\cos 2x\right|\Rightarrow f\left(x\right)=\{\begin{array}{c}\begin{array}{cc}-\cos 2x& x>\pi /4\end{array}\\ \begin{array}{cc}\cos 2x& x\le \pi /4\end{array}\end{array}\Rightarrow f^{\prime }\left(x\right)=\{\begin{array}{c}\begin{array}{cc}2\sin 2x& x>\pi /4\end{array}\\ \begin{array}{cc}-2\sin 2x& x\le \pi /4\end{array}\end{array}$
Hence $f^{\prime }(\frac{\pi }{4}+0)=2$