Differential Geometry - Computation Help I'm trying to learn differential geometry through one of MIT's online courses (lecture notes found here:  http://ocw.mit.edu/courses/mathematics/18-950-differential-geometry-fall-2008/lecture-notes/ch1_revised.pdf) and am stuck with what should be an easy question.  The question asks to show the following:  Suppose $c(s)$ is a regular curve ($c'(s) \ne 0$) in the plane with $|c(s)| \le 1$ and suppose there is a point t with $|c(t)| = 1$.  Then $|\kappa(t)| \ge 1$.  Here, $\kappa$ is defined as 
$\frac{det(c', c'')}{||c'||^3}.$
It's should be straightforward if we write $c$ as the graph of a function and rotate so that $c(t) = (0,1)$.  However, I feel as if there should be a more elegant solution using only what's found in the first day's notes (found in the link).  I just don't see it.    

Geometrically, you should understand that if the curve $c$ stays inside the unit circle and touches at a point, it must be at least as curved as the circle at that point. 
Here's a hint: Use the fact that $t$ is a local maximum of the function $|c(s)|^2$, and put your calculus to work :)
