Let ƒ : [0, 2] $ \to $ R be a twice differentiable function such that ƒ''(x) > 0, for all x $ \in $ (0, 2). If $\phi $(x) = ƒ(x) + ƒ(2

Question

Let ƒ : [0, 2] $ \to $ R be a twice differentiable function such that ƒ''(x) > 0, for all x $ \in $ (0, 2). If $\phi $(x) = ƒ(x) + ƒ(2 – x), then $\phi $ is :

decreasing on (0, 2)

decreasing on (0, 1) and increasing on (1, 2)

increasing on (0, 2)

increasing on (0, 1) and decreasing on (1, 2)

Solution

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