Mathematics - Differentiation Question with Solution | TestHub

$\text{f}\left(\text{x}\right)=\text{x sin }\pi \text{x},\text{x}>0$

As $f\text{'}\left(x\right)$ vanishes,
${\text{f}}^{\prime }\left(\text{x}\right)=\text{sin }\pi \text{x}+\pi x\; cos\pi \text{x}=0$
$\text{tan}\pi \text{x}=-\pi \text{x}$

We will draw the graph of $\mathrm{tan\pi }x \& -\mathrm{\pi x}$.

And their intersection points will be the points, where $f\text{'}\left(x\right)$ vanishes.