(a) Suppose that the tangent line to the curve y = f (x) at the point (3, -11) has equation y = -5 - 2x. If Newton's method is used to locate a root of the equation f (x) = 0 and the initial approximation is x1 = 3, find the second approximation x2.
(b) Suppose that Newton's method is used to locate a root of the equation f (x) = 0 with initial approximation x1= 9. If the second approximation is found to be x2 = -6, and the tangent line to f (x) at x = 9 passes through the point (18, 5), find f (9).
(c) Use Newton's method with initial approximation x1 = 4 to find x2, the second approximation to the root of the equation x3 = 7x + 5.