For all twice differentiable functions f : R $\to$ R,
with f(0) = f(1) = f'(0) = 0
Solution
f : R $\to$ R, with f(0) = f(1) = 0
<br>and f'(0) = 0
<br>$\because$ f(x) is differentiable and continuous
<br>and f(0) = f(1) = 0
<br><br>Applying Rolle’s theorem in [0, 1] for function f(x)
<br>f'(c) = 0, c $\in$ (0, 1)
<br><br>Now again
<br>$\because$ f'(c) = 0, f'(0) = 0
<br>again applying Rolles theorem in [0, c] for function f'(x)
<br>f''(c<sub>1</sub>) = 0 for some c<sub>1</sub> $\in$ (0, c) $\in$ (0, 1)
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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