Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Iteration 1:

Iteration 2:

Step-by-step explanation:

Formula for Newton's method is,

Given the initial guess as , therefore value of n = 1.

Also, .

Differentiating with respect to x,

Applying difference rule of derivative,

Applying power rule and constant rule of derivative,

Substituting the value,

Calculating the value of and

Calculating

Calculating ,

Substituting the value,

Therefore value after second iteration is

Now use as the next value to calculate second iteration. Here n = 2

Therefore,

Calculating the value of and

Calculating

Calculating ,

Substituting the value,

Therefore value after second iteration is