Thank you for your astute observation on my derivation. Yes I left an 'x' out of differentiation. Since x =1 it does not affect the final conclusion.

I will be highly obliged if you could elucidate on the two exponential limilts you have mentioned. What would the curve eqn. be and how did you arrive at the limits? It will be very interesting and valuable to me

All the best,

Mally