Exercise 5

In[31]:=

  Clear[f]
  f[x_] := (x - 1) Exp[-x]

We don't need Mathematica to find the zero of this function, but let's see how Newton's method handles it anyway. Graph the function for 0 < x < 5. Can you predict the behavior of Newton's method with an initial guess of 3? Explain your prediction. Try it to confirm your prediction.

Moral: Starting values have to be sufficiently accurate to guarantee convergence.

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