Since y/p will always be positive for positive values of p, and (n-y)/(1 - p) will always be negative for sufficiently large positive values of p, as p increases, (y/p) - (n-y)/(1 - p) is always positive.
So, the rate of change is always positive, the original expression has no maximum value for p.
Except.. this hand out seems to be quite adamant about the fact that there is a maximum.
If (y/p) were to = (n-y)/(1 - p), then the derivative expression would be zero.
So, i set them equal to one another and solved for p, p = y/n
However when I go back and check that (y/p) - (n-y)/(1 - p) evaluates to zero for p = y/n, I find that it doesn't.
Is my logic unsound here somewhere?
Thank you for your help TKHunny