### Home > APCALC > Chapter 8 > Lesson 8.4.1 > Problem 8-141

Without looking at the graph, use Newton’s Method to approximate the roots of . What happened?

What happened?

Think about the shape of the graph of .

What is its range? What does that mean about the roots?

**Newton's Method for Approximating Roots**

**Newton’s Method** uses an iterative process to approximate a root (-intercept) of a function.

Begin with a point

*near the root. Write the equation of its tangent line at*

*.*

The -intercept of this tangent line is

*.*

Solve for

*by setting*

*.*

, solve for the root of the line tangent to

*at*

*. This process continues until the desired accuracy is met.*

Therefore, each new approximation, , can be found using