Question:

Let f(x) = sin(πx/x²), x > 0. Let x₁ < x₂ < x₃ < ... < xₙ < ... be all points of local maximum of f and y₁ < y₂ < y₃ < ... < yₙ < ... be all the points of local minimum of f. Then which of the following option(s) is/are correct?

|xₙ - yₙ| > 1 for every n

xₙ₊₁ - xₙ > 1 for every n

xₙ ∈ (2n, 2n + 1/2) for every n

x₁ < y₁

Correct option is D. xₙ ∈ (2n, 2n + 1/2) for every n
f'(x) = 2x cos(πx) (πx/2 - tan(πx))/x⁴