Let $\phi(x) = f(x) + f(1-x)$ and $f^{\prime \prime}(x) < 0$ in $[0, 1]$, then

• A
  $\phi$ is monotonic increasing in $\left[0, \frac{1}{2}\right]$ and monotonic decreasing in $\left[\frac{1}{2}, 1\right]$
• B
  $\phi$ is monotonic increasing in $\left[\frac{1}{2}, 1\right]$ and monotonic decreasing in $\left[0, \frac{1}{2}\right]$
• C
  $\phi$ is neither increasing nor decreasing in any sub-interval of $[0, 1]$
• D
  $\phi$ is increasing in $[0, 1]$