Differential Geometry: Show Regular Curve is Invertible

[whynothis]

Hello all,

I am taking a class on differential geometry and I have run into a problem with the following question:

Show that if α is a regular curve, i.e., ||α'(t)|| > 0 for all t ∈ I, then s(t) is an invertible function, i.e., it is one-to-one (Hint: compute s'(t) ).

I am not really sure what the hint is getting at and don't really know how I should be aproaching this problem.
Any help would be greatly appreciated : )

thanks in advanced!

 

[HallsofIvy]

Perhaps it would be a good idea to say what relation the curve α has to s(t)! Are we to assume that s(t) is the arclength of a portion of α?

 

[whynothis]

Right, my appologies. s(t) is the arclength of the curve relative to some point say t=a.