Question

If $y = | \cos\, x | + | \sin\, x |$, then $\frac{dy}{dx}$ at $x = \frac{2 \pi}{3}$ is

• A. $\frac{1 - \sqrt{3}}{2}$
• B. $0$
• C. $\frac{1}{2} ( \sqrt{3} - 1)$
• D. $None\, of\, these$

Answer 1

Answer: (C)

We have, $y = | \cos\, x | + | \sin\, x |$
At $x = \frac{2 \pi}{3} , \cos \, x$ is -ve and $\sin \, x $ is +ve
$\therefore \:\:\:\: y = -\cos \, x + \sin \, x$
$\Rightarrow \:\: \frac{dy}{dx} = \sin \, x + \cos \, x$
$\therefore \:\: \frac{dy}{dx} \bigg|_{at \, x = 2 \pi / 3} = \sin \bigg( \frac{2 \pi}{3} \bigg) + \cos \bigg( \frac{2 \pi}{3} \bigg) $
$ = \frac{\sqrt{3}}{2} - \frac{1}{2} = \frac{\sqrt{3} - 1}{2} $