Suppose the line y = 4x - 1 is tangent to the curve y = f(x) when x = 1. If Newton's method is used to locate a root of the equation f(x) = 0 and the initial approximation is x1 = 1, find the second approximation x2.
Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Round your answer to four decimal places.)
Use Newton's method with initial approximation x1 = -1 to find x2, the second approximation to the root of the equation x3 + x + 3 = 0.
Use Newton's method to find all roots of the equation correct to six decimal places. ex = 8 - 3x