Prove the following

Question:

Let $f:[0,2] \rightarrow \mathrm{R}$ be a twice differentiable function such that $f^{\prime \prime}(\mathrm{x})>0$, for all $\mathrm{x} \in(0,2)$. If $\phi(x)=f(x)+f(2-x)$, then $\phi$ is :

  1. decreasing on $(0,2)$

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

  3. increasing on $(0,2)$

  4. increasing on $(0,1)$ and decreasing on $(1,2)$


Correct Option: , 2

Solution:

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