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Let $$f(x) = x \sin \pi x, x > 0$$ Then for all natural numbers n, $$f'(x)$$ vanishes at
a unique point in the interval $$\left(n, n + \frac{1}{2}\right)$$
a unique point in the interval $$\left(n + \frac{1}{2}, n + 1\right)$$
a unique point in the interval $$(n, n + 1)$$
two points in the interval $$(n, n + 1)$$
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