Four different methods were used to solve ( ) = 0, and the computed values for 1 , 2 , 3 , ··· are shown in Table 2.11. (a) One of them is Newton’s method. Which of the four is most likely Newton’s...

Four different methods were used to solve
() = 0, and the computed values for

₁,

₂,

₃, ··· are shown in Table 2.11.

(a) One of them is Newton’s method. Which of the four is most likely Newton’s method, and why?

(b) One of them is the bisection method. Which of the four is most likely the bisection method, and why?

(c) Suppose someone claimed they computed the solution using the secant method, and they obtained the results given for Method 3. Why would you tell them that they are most likely mistaken (i.e., they are wrong)?