Use Newton's Method and continue the process until two successive approximations differ by less than 0.001.

Question

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero'(s) using a graphing utility and compare the results.

f (x) = x^3 + x - 1

Answer 1

Step 1:

The function

Differentiate on each side with respect to .

Newton's approximation method formula :  .

Consider

Step 2:

Step 3:

Graph :

Observe the graph zeros of the function is 0.682.

Solution:

Zero of the function is 0.682.