3. Let f(x) = 2³ px - q with p = 3 × 2-18 and q = 2. The only real root of this equation is

r≈ 1.25992407762209935560844934660

(a) Use Newton's method to approximate this root starting with the initial guess x0 = 1. How

many iterations are required before |h| = | − f(n)| ≤ mach?

(b) Use the secant method to approximate the root, starting with the initial guesses x = 1

and ₁= 2. How many iterations are required before |h| = |- f(n) |

(c) Run Newton's method for this function for a few steps starting with co = 0.1 and comment

on the results.

(d) Run Newton's method for this function starting with zo = 0.2 and comment on the results.