QUESTION 3 (3.1) (12) Obtain the extremals (if they exist) of the following problem of Lagrange with functional I[X] = $2 + 8xdt, subject to the following auxiliary and boundary conditions: x+ y=0, x(0) = 0, y(0) = 1, x(2) = 10, y(2) = -9. (3.2) We know that for L = L(t, x, i), the Euler-Lagrange equation is calculated by (10) d OL OL at = 0. Ox Show that the if L = f(t, x) v1 + x2, where f(t, x) be a known function of t and x(t), then the Euler- Lagrange equation gives ic ft + where ft = of 1 +72 - fx = 0, at and fx = of ax [22]