Find a curve with constraints
Hello,
I am trying to find the steepest curve f(x) constrained so that if we consider a segment [AB] with its edges on the curve (A = f(x=a), B = f(x=b)) and with [AB] length = L , the distance between f(x) and the AB segment is < h, with "h" and "L" known.
My maths knowledge faded away - I'm looking for some help on how to approach this - and then to see if it's something where Sage can assist on. Thanks!
Sounds like a theoretic problem irrelevant to Sage.
What does it mean "steepest"? For instance, if $A=(0,0)$, $B=(1,0)$, $f:[0,1]\to[0,1]$ with $f(0)=f(1)=0$ and $h=1$, among the many continuous $f$-functions which is the one we want?