Question:
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
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
Updated On: Oct 1, 2024
- f' is continuous at x = 0
- f' is differentiable at x = 0
- ff′ is differentiable at x = 0
- (f′)2 is differentiable at x = 0
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The Correct Option is A, C, D
Solution and Explanation
The correct option is (A) : f' is continuous at x = 0, (C) : ff′ is differentiable at x = 0 and (D) : (f′)2 is differentiable at x = 0.
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