4. Numerical Analysis

Root Finding — Quiz

Test your understanding of root finding with 5 practice questions.

Practice Questions

Question 1

When analyzing the convergence of root-finding methods, what does it mean for a method to have an order of convergence $p > 1$?

Question 2

Consider the function $f(x) = x^3 - 2x - 5$. If we apply Newton's Method with an initial guess of $x_0 = 2$, what is the value of the next approximation $x_1$?

Question 3

The Secant Method's convergence rate is often described as superlinear. Which of the following values best approximates its order of convergence?

Question 4

Which of the following scenarios would most likely lead to slow convergence or divergence of the Bisection Method?

Question 5

Consider the function $f(x) = \cos(x) - x$. If we use Newton's Method with an initial guess $x_0 = 0.5$, what is the value of $f'(x_0)$?