### Home > CALC3RD > Chapter Ch7 > Lesson 7.3.5 > Problem 7-159

Use Newton’s Method to calculate the -intercept of the function

*, correct to five decimal places.*

A reasonable estimate is .

**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