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**Rescription** I need to find/make a function, f(x), such that:

f(0)=h

f(x) > 0 along x(0,1)

f ' (x) < 0 along x:(0,1)

f(1) is negligible (f(1)<<h/10000) or f(1)=0

f ' (1) is negligible or 0

Integral from 0 to 1 of f(x) dx = 1

f ' ' (c)=0 c:(0,1) (that's second deriv if you can't read it)

f ' ' (x)<0 x:(0,c)

f ' ' (x)>0 x:(c,1)

So basically a nice smooth curve along x:[0,1] starting at f(0)=h and headed slowly downward, quickly downward at x=c, then slowly downward to essentially 0 when x=1.