PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Continuity & Differentiability
Let f : (−1, 1) → ℝ be a differentiable function satisfying f(0) = 0. Suppose there exists an M > 0 such that |f′(x)| ≤ M|x| for all x ∈ (−1, 1). Then
1
f′ is continuous at x = 0
2
f′ is differentiable at x = 0
3
f f′ is differentiable at x = 0
4
(f′)2 is differentiable at x = 0