For all twice differentiable functions f: R → R, with f(0) = f(1) = f'(0) = 0,
For all twice differentiable functions f: R → R, with f(0) = f(1) = f'(0) = 0,
Option 1 -
f''(x) ≠ 0, at every point x ∈ (0,1)
Option 2 -
f''(x) = 0, for some x ∈ (0,1)
Option 3 -
f''(0) = 0
Option 4 -
f''(x) = 0, at every point x ∈ (0,1)
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:Applying Rolle's theorem in for function f (x), there exists c such that f' (c) = 0, c ∈ (0,1).
Again applying Rolle's theorem in [0, c] for function f' (x), there exists c? such that f' (c? ) = 0, c? ∈ (0, c).
Option A is correct.
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