Select the first function, f(x) = 0.1x3 − 0.1x2 − 0.2x + 0.1. (a) if you begin newton's method with the initial approximation x1 = −2.5, how many approximations are required to reach a function value of 0. (rounded to 5 decimal places)? what is the approximate root? (give your answer to six decimal places.) x = (b) with x1 = −0.64, what does newton's method give for x2? x2 = explain why the method produced a worse approximation to the nearest root than x1. this answer has not been graded yet. how many approximations are required to determine the root accurate to 5 decimal places? (c) approximate the root closest to the origin to 5 decimal place accuracy. x =