Choose two cubics, one of the form , with , and the otherOriginally Posted by MathsThief
, with .
Arrange for the first to have a local minimum at , and the
second to have a local maximum at the same point, and then arrange that the
two curves are equal at the point. Then if this point is the join the merged curve will be smooth.
Now arrange for the total length of the merged curve to be 20km