Well, to me, the peak seems to be the highest possible value. Am I doing something wrong?

I wrote a program to find the peak, using your formula. It seems to peak the higher I go. Change stp to work in different increments. 99.99999999999996% seems peak with lousy double precision.
I'm not sure why my results contradict yours, unless I'm using the wrong x value or t1 value, but it doesn't seem to make a difference.
Regards,
Michael

CLS
DEFDBL A-Z
c = 300000
stp = 1 'change this value to adjust step
lower = c - stp * 1000
upper = c - stp
t1 = 1
best = 0
x = 1
FOR v = lower TO upper STEP stp
 t2 = (t1 - v / c ^ 2 * x) / SQR(1 - v ^ 2 / c ^ 2)
 'find highest t2 value in range
 IF t2 > best THEN best = cur: btrk = v
NEXT v
PRINT t1; t2; best; btrk; STR$((btrk / c) * 100); "%"