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

Answer: (B)

$\frac{1}{\sqrt{2}}$

When $\frac{\pi }{2}<x<\pi ,\cos x<0$
$\therefore |\cos x|=-\cos x$
$\therefore f\left(x\right)=-\cos x$
$\Rightarrow f^{\prime }\left(x\right)=\sin x$
$\therefore f^{\prime }\left(\frac{3\pi }{4}\right)=\sin \frac{3\pi }{4}$
$=\frac{1}{\sqrt{2}}$