Let $R=\left\{(x,t): 0<x<1,0<t<T\right\}$ and let $u(x,t)\in C_1^2 (\bar{R})$ be a solution of $$u_t=u_{xx}-x^2 u \hskip 5pt in \hskip 5pt R$$ $$u_x(0,t)=0, 0\leq t \leq T$$
a) Show that the maximum of $u(x,t)$ in $\bar{R}$ must occur at t$=0$ or $x=1$.
I think we should reflect the solution across the t axis. But I don't know how to do it exactly, could anyone help?