That is a standard "Calculus of Variations" problem.
want to prove that the lone segment[P,Q] is the shortest curve going from P to Q. Consider a piecewise differentiable curve y ,[IMG]file:///C:/DOCUME%7E1/libguest/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG] going from P to Q. We want to show that the euclidean length (y) is greater than or equal to the euclidean length ([P,Q]) of the line segment [P,Q].
a. First consider the case where P= (X0,Y0) and Q= (X0,Y1) sit on the same vertical line of equation X= X0. Show hat the euclidean length is greater than or equal to
lY1-Y0 l = euclidean length([P,Q])
This problem has been racking my brains. Any help will greatly be appreciated