Answer
There is an antinode at $x = 0$
Work Step by Step
$y'(t) = (3~mm)~sin(5x+\frac{\pi}{2})~cos(4t)$
We can find the amplitude of the standing wave at $x = 0$:
$A = (3~mm)~sin(5x+\frac{\pi}{2})$
$A = (3~mm)~sin(0+\frac{\pi}{2})$
$A = (3~mm)(1)$
$A = 3~mm$
This is the maximum possible amplitude for this standing wave.
There is an antinode at $x = 0$
