Question: Now you will approximate the zeroes of \(f\left( x \right)={{x}^{3}}-x-1\) using the Newton's Method Strategy with several different initial guesses:

1. First use the initial guess to the zero as x ₀ =1
   Use Newton's Method to generate the zero of the function to 6 decimal place accuracy. Record all calculation.
2. Now try initial guess to the zero as x 0 =0.6
   Use Newton's Method to generate the zero of the function to 6 decimal place accuracy. Record all calculation.
3. Now try the initial guess to the zero as x 0 =0.57
   Use Newton’s Method to generate the zero of the function to 6 decimal place accuracy. Record all calculation
4. Conjecture why the three different initial guesses affected the outcome of Newton's Method, i.e. why Newton's Method is so sensitive to the initial approximations. Note how many interactions were needed in each of the three initial guess cases above. Look at the graphs and initial locations of the tangent lines as part of your analysis.

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