For all twice differentiable functions f : R $ \to $ R, with f(0) = f(1) = f'(0) = 0

Question

For all twice differentiable functions f : R $ \to $ R,
with f(0) = f(1) = f'(0) = 0

f''(x) $ \ne $ 0, at every point x $ \in $ (0, 1)

f''(x) = 0, for some x $ \in $ (0, 1)

f''(0) = 0

f''(x) = 0, at every point x $ \in $ (0, 1)

Please login to view the detailed solution steps...