JEE Main 2021 Mathematics question

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

• (A)f''(x) = 0 for all x(0, 2)
• (B)f''(x) = 0 for some x(0, 2)Correct
• (C)f'(x) = 0 for some x[0, 2]
• (D)f''(x) > 0 for all x(0, 2)