Which of the following statements applies to the bisection method used for…
1998
Which of the following statements applies to the bisection method used for finding roots of functions?
- A.
converges within a few iterations
- B.
guaranteed to work for all continuous functions
- C.
is faster than the Newton-Raphson method
- D.
requires that there be no error in determining the sign of the function
Show answer & explanation
Correct answer: D
The bisection method works by maintaining an interval [a, b] such that f(a) and f(b) have opposite signs. At each step, the midpoint is tested and the sign of the function value decides which half of the interval still brackets the root. Therefore, the method depends on correctly determining the sign of the function. It is not necessarily fast, it is not guaranteed for every continuous function without a bracketing interval, and it is usually slower than Newton-Raphson when Newton-Raphson converges. Hence, option D is correct.