Let y : ℝ → ℝ be a twice differentiable function such that y′′ is continuous on [0, 1] and y(0) = y(1) = 0. Suppose y′′(x) + x2 < 0 for all x ∈ [0, 1]. Then
1
y(x) > 0 for all x ∈ (0, 1)
2
y(x) < 0 for all x ∈ (0, 1)
3
y(x) = 0 has exactly one solution in (0, 1)
4
y(x) = 0 has more than one solution in (0, 1)