Suppose we have a laterally insulated rod and the temperature satisfies $u_t = a^2 u_{xx}$. Suppose near some point $x_0$ and at some time $t_0$, the solution is concave down. What is true about the solution $u$ near $x_0$ at time $t_0$. There may be more than one correct answer. Use your intuition.

A. It is decreasing as time goes on.

B. It is increasing as time goes on.

C. It is necessarily negative at that point.

D. It is staying constant as time goes on.

E. It is necessarily positive at that point.

F. None of the above