I was reading the chapter on Fermat's principle in the Feynman lecture series. The principle is stated along these lines:
"The correct statement is the following: a ray going in a certain particular path has the property that if we make a small change (say a one percent shift) in the ray in any manner whatever, say in the location at which it comes to the mirror, or the shape of the curve, or anything, there will be no first-order change in the time; there will be only a second-order change in the time. In other words, the principle is that light takes a path such that there are many other paths nearby which take almost exactly the same time"
Could someone please explain what "no first-order change in the time" means here?