. A variant of the secant method defines two sequences u and vk such that f(u) has one sign and f(%) has the opposite sign. From these sequences and the secant mothod one can derive the expression ue = uk/u)-rkf(uk), k = 1,2,3, f(vx) (k) We define uk +1 vk and vk +1 = t/k if f(tok)f(uk) > 0 and uk +1 1k and vk +1 vk otherwise. Suppose that f" is continuous on the interval uo, vol and that for some K, f" has a constant sign in uK,vK]. Explain why either K for al k2 K or vk -vK for all k2 K. Deduce that the methods converges lincarly