Question

If $f\left(x\right)=|\cos x|$ then $f^{\prime }\left(\frac{3\pi }{4}\right)$ is equal to-

• A. $-\frac{1}{\sqrt{2}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $1$
• D. None of these

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

Clearly, $\frac{\pi }{2}<\frac{3\pi }{4}<\pi \Rightarrow \cos x<0$ in this interval
$\therefore y=-\cos x$
$\Rightarrow \frac{dy}{dx}=\sin x$

$\Rightarrow {\left(\frac{dy}{dx}\right)}_{3\pi /4}=\sin \frac{3\pi }{4}=\frac{1}{\sqrt{2}}$