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Let g : R → R be a non constant twice differentiable function such that g ′ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 1 = g ′ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 3 . If a real valued function f is defined as ƒ(x) = 2 1 [g(x) + g(2 – x)], then

1. ƒ ′′ (x) = 0 for exactly one x in (0, 1)
2. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ′ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ′ 2 1 ƒ 2 3 ƒ = 1
3. ƒ ′ (x) = 0 for atleast two x in (0, 2)
4. ƒ ′ (x) = 0 for no x in (0, 1)

Correct answer: ƒ ′ (x) = 0 for atleast two x in (0, 2)

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