(1) Let u() be an extremal (e.g. minimizer) of the functional F[u(-)] = L(x, u(x), u'(x))dx. Find the Euler-Lagrange equation satisfied by u() where L(x,z,p) is given by the following functions: (a) L(x,z,p)=xz +p² (b) L(x,z,p)=√1+p² (c) L(x,z,p) + xp² (d) L(x,z,p) xp - p²