Answer
$\frac{di}{dt}~~$ reaches a maximum when $~~t = \frac{T}{2}$
Work Step by Step
We can write an expression for the current:
$i = -\omega~Q~sin(\omega t+\phi)$
At $t=0$, the capacitor is charged, so $U_E$ is a maximum and the current $i = 0$
Therefore, $\phi = 0$
We can write an expression for the current:
$i = -\omega~Q~sin(\omega t)$
$\frac{di}{dt} = -\omega^2~Q~cos(\omega t)$
$\frac{di}{dt}$ reaches a maximum when $\omega t = \pi$
$t = \frac{\pi}{\omega} = \frac{T}{2}$
Therefore:
$\frac{di}{dt}~~$ reaches a maximum when $~~t = \frac{T}{2}$
