Exercise · ZW-SECANT-METHOD-008 · ★★☆ Intermediate
For \(f(x)=x^2-2\) with \(x_0=1\) and \(x_1=2\), what is \(x_2\)?
Choose one option.
Show answer
- B. \(4/3\)
Explanation
Use x_2=2-f(2)(2-1)/(f(2)-f(1))=2-2·1/3=4/3. Using the midpoint 3/2 is a frequent error.
Review the concept: Secant method
The secant method is an iterative procedure for approximating roots of a function \(f(x)=0\) using two previous approximations, without needing to compute the derivative.
\[x_{n+1}=x_n-f(x_n)\frac{x_n-x_{n-1}}{f(x_n)-f(x_{n-1})}\]
More practice problems: secant method
- ZW-SECANT-METHOD-001 Which method replaces Newton-Raphson's derivative with a difference quotient?
- ZW-SECANT-METHOD-002 How many starting values does the secant method need?
- ZW-SECANT-METHOD-003 What geometric object defines the secant step?
- ZW-SECANT-METHOD-004 What happens if f(x_n)=f(x_n-1) in the formula?
- ZW-SECANT-METHOD-005 Approximately what order of convergence does the secant method have?
- ZW-SECANT-METHOD-006 With f(x)=x^2-4, x_0=1 and x_1=3, what is x_2 under the secant method?
- ZW-SECANT-METHOD-007 If f(x)=x^3-x-2 with x_0=1 and x_1=2, what is f(x_1)-f(x_0)?
- ZW-SECANT-METHOD-009 Which initial condition should be checked before iterating with the secant method?