If $\phi(x) = f(x) + f(1-x), f’(x)<0 \: for\: 0 \leq x \leq 1$, then the tautology among the following is

Question

$\begin {array} {1 1} (A)\;\phi(x)\: is \: increasing \: in\: \bigg[0,\large\frac{1}{2} \bigg] & \quad (B)\;\phi(x)\: is\: decreasing \: in\: \bigg[0,\large\frac{1}{2} \bigg] \\ (C)\;\phi(x)\: is \: increasing \: in\: \bigg[ \large\frac{1}{2},1 \bigg] & \quad (D)\;\phi(x)\: has\: minima\: at\: x=\large\frac{1}{2} \end {array}$