Question

If f(x) = |cos x|, then the value of $f\text{'}\left(\frac{3\pi }{4}\right)$ is

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $-\frac{1}{\sqrt{2}}$

Answer 1

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

$\mathrm{When}\frac{\pi }{2}<x<\pi ,\cos x<0\mathrm{so}\mathrm{that}\left|\cos x\right|=-\cos x\Rightarrow f\text{'}\left(x\right)=\sin x\mathrm{Hence},f\text{'}\left(\frac{3\pi }{4}\right)=\sin \frac{3\pi }{4}=\frac{1}{\sqrt{2}}$