Let $f\left(\text{x}\right)=\text{x }\text{sin }\pi \text{x}$, $\text{x}>0$. Then for all natural numbers $\text{n}\text{, }{f}^{\prime }\left(\text{x}\right)$ vanishes at

• A

  A unique point in the interval $\left(\text{n}\text{, }\text{n}+\frac{1}{2}\right)$
• Correct answer
  B

  A unique point in the interval $\left(\text{n}+\frac{1}{2}\text{, }\text{n}+1\right)$
• Correct answer
  C

  A unique point in the interval (n, n + 1)
• D

  Two points in the interval (n, n + 1)

Hence, the correct answer is options: 'B', 'C'.