What you have done is plain great. Congratulations!

Not even knowing you much, I sincerely wish you all the good.

Mazel Tov! Best of luck with your new daughter.

Maybe you should just ignore the day/night thing for a couple of weeks, go to split-sleep or something. ;-)

deriving

f(x)=K*(x-a)*(x-b)*(x-c) using the product rule we get f'(x)=
K*((x-a)*(x-b)+(x-a)*(x-c)+(x-b)*(x-c))=

K*((x-a)*(x-b)+(x-c)*(2x-a-b))

taking x=v=(a+b)/2 the second term vanishes and we have

f'(v)= K*(v-a)*(v-b)

the crossing point should be

v - f(v)/f'(v)

as in Newton's method and in this case:

v - (v-c)=c

A baby! Yay!

Enjoy -- if you're lucky, you just keep thinking every age is the very best. We're up to 16 yo on the oldest and while it's definitely not the same fun as having a baby, it's still pretty fun!

Or should I have said,

Hi *dad* -- are you sleeping? Things sure are going to be different, you can't even imagine.

;-D

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