Question

The subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is

• A. 0
• B. 1
• C. $\pi/2$
• D. none of these

Answer 1

The Correct Option is C

$y=x\,sin\,x$
$\Rightarrow \frac{dy}{dx}=x\,cos\,x+sin\,x\cdot1=x\,cos\,x+sin\,x$
At $x=\frac{\pi}{2}, \frac{dy}{dx}=0+sin \frac{\pi}{2}=1$
and $y=\frac{\pi}{2} sin \frac{\pi}{2} =\frac{\pi}{2}$
Now subtangent $=\left|\frac{y}{y_{1}}\right|_{at\,x=\pi/2}=\frac{\pi/2}{1}=\frac{\pi}{2}$