(4) Most variational problems tend to depend upon a function u and its derivative u'. An equation analogous to the Euler-Lagrange equation can be derived for problems involving the second derivative u". Derive this equation by working through the variation principles outlined in the lecture notes. The only thing new in this question is the additional term in the expansion of the variation of the functional due to the dependence on u". State any assumptions you make in the derivation. (NOTE: for physical problems where a system depends upon the third time derivative of a we must use this generalized mechanics, and these problems are called "jerky", jerk being the time derivative of the acceleration.)