In this problem assume that ( ) satisfies the conditions of Theorems 2.2 and 2.3. (a) Suppose it is claimed that the values in Table 2.2 were produced using Newton’s method. What argument can you make...

In this problem assume that
() satisfies the conditions of Theorems 2.2 and 2.3.

(a) Suppose it is claimed that the values in Table 2.2 were produced using Newton’s method. What argument can you make to refute this claim?

(b) Suppose it is claimed that the values in Table 2.7 were produced using the bisection method. What argument can you make to show this is unlikely?

(c) When using the secant method, does it make any difference which point is labeled

₀
and which is labeled

₁? In particular, what happens to

₂
and

₃
if you switch which point is labeled
₀
and

₁?