Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then

Question

f''(x) = 0 for all x $\in$ (0, 2)

f''(x) = 0 for some x $\in$ (0, 2)

f'(x) = 0 for some x $\in$ [0, 2]

f''(x) > 0 for all x $\in$ (0, 2)

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