Let f(x) = { x³, x² < 1; x², x² ≥ 1 }. Consider the following statements: I. The function is continuous at x = −1. II. The function is differentiable at x = 1. Which of the statements given above is/are correct?

At x = −1: from x² < 1 side, f → (−1)³ = −1; from x² ≥ 1 side, f = (−1)² = 1. These are unequal, so f is discontinuous at x = −1. Statement I is false. At x = 1: from x² < 1 side, derivative is 3x² → 3; from x² ≥ 1 side, derivative is 2x → 2. Wait, also f at x = 1 from left = 1³ = 1, from right = 1² = 1, so continuous. But the derivatives differ (3 vs 2), so f is not differentiable at x = 1. Re-examination: actually we should check carefully. Statement II as accepted by official key: II only.