Let $$f(x) = x \sin \pi x, x > 0$$ Then for all natural numbers n, $$f'(x)$$ vanishes at

A

a unique point in the interval $$\left(n, n + \frac{1}{2}\right)$$

B

a unique point in the interval $$\left(n + \frac{1}{2}, n + 1\right)$$

C

a unique point in the interval $$(n, n + 1)$$

D

two points in the interval $$(n, n + 1)$$