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Limits Continuity and Differentiability question

2021 · 31 Aug · Shift 2 · Q34

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JEE Main
Mathematics
Limits Continuity and Differentiability
2021 · 31 Aug · Shift 2 · Q34

Limits Continuity and Differentiability question

2021 · 31 Aug · Shift 2 · Q34

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

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 $\in$ (0, 2)
B
f''(x) = 0 for some x $\in$ (0, 2)
C
f'(x) = 0 for some x $\in$ [0, 2]
D
f''(x) > 0 for all x $\in$ (0, 2)

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