PG entrance exam IIT JAM 2025 Mock Test Mathematics Quadratic Equations Location of Roots

Let f : ℝ → ℝ be an infinitely differentiable function such that f′′ has exactly two distinct zeroes. Then

1
f′ has at most 3 distinct zeroes
2
f′ has at least 1 zero
3
f has at most 3 distinct zeroes
4
f has at least 2 distinct zeroes
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