# Question #90cf3

##### 2 Answers

To find the roots of equations like

#### Explanation:

Let's do an example.

To use Newton's method, you write the equation in the form

Compute

Because the method requires that we do the same computation many times, until it converges, I recommend that you use an Excel spreadsheet; the rest of my answer will contain instructions on how to do this.

Enter a good guess for x into cell A1. For this equation, I will enter 2.

Enter the following into cell A2:

=A1-(EXP(A1) - A1^3)/(EXP(A1) - 3*A1^2)

Please notice that the above is Excel spreadsheet language for

Copy the contents of cell A2 into A3 through A10. After only 3 or 4 recursions, you can see that the method has converged on

We can use the Intermediate Value Theorem to see that each pair has at least one point of intersection.

#### Explanation:

At

At

At

At

(Note that