Question

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

• A. y(x) > 0 for all x ∈ (0, 1)
• B. y(x) < 0 for all x ∈ (0, 1)
• C. y(x) = 0 has exactly one solution in (0, 1)
• D. y(x) = 0 has more than one solution in (0, 1)

Answer 1

Answer: (A)

y(x) > 0 for all x ∈ (0, 1)

Answer 2

The correct option is (A) : y(x) > 0 for all x ∈ (0, 1).