# Homework Help: Minimizing a curve

1. Mar 30, 2009

### Kreizhn

I've been given a continuously differentiable function C(u1, u2) in 2-D Euclidean space. Now i have that for u a function of s, that
$$\frac{ dC}{ds} = \frac{\partial C}{\partial u_1}\frac{ du_1}{ds} + \frac{ \partial C}{\partial u_2} \frac{ du_2}{ds}$$
which is obviously just an extension of the chain rule. Now I'm told to minimize this subject to the constraint that
$$\left( \frac{\partial u_1}{\partial s} \right)^2 + \left( \frac{\partial u_2}{\partial s} \right)^2 = 1$$
and given that the answer is
$$\frac{ du}{ds} = - \frac1{\left\| \frac{\partial C}{\partial u} \right\| } \frac{\partial C}{\partial u}$$

My problem is that I don't see how we arrived at the answer. What am I missing?