f(x) = x^3 - x - 4
f'(x) = 3x^2 - 1

Interval: [4/9,2]
Must use initial approximation as: x = 2/3 ∈ [4/9,2]
I already checked the Newton's Method hypotheses. I sub in (2/3) = x0 into the Newton's Method equation and correct me if I am wrong, but I am getting x-values that are significantly away from the interval itself (in the negatives). What am I doing wrong?

Question

f(x) = x^3 - x - 4 
f'(x) = 3x^2 - 1 

Interval: [4/9,2]
Must use initial approximation as: x = 2/3 ∈ [4/9,2]
I already checked the Newton's Method hypotheses. I sub in (2/3) = x0 into the Newton's Method equation and correct me if I am wrong, but I am getting x-values that are significantly away from the interval itself (in the negatives). What am I doing wrong?

anonymous · Answer

By the way, the question says: (b) Solve the equation in part (a) using x1 = 0.6 as the initial approximation. The equation in part (a) I have already given in my opening post

anonymous · Answer

Check your steps against the ones shown here: http://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx I feel following his steps for this would really help you find your error. Your derivative, f'(x), is correct.

anonymous · Answer

Double check the original function too, just in case

anonymous · Answer

Look for incorrect +'s or -'s