2.13 Newton's Method: Quiz

Problem 5

Why does each of the following problems fail using Newton's Method?

  1. Find a solution to x2 + 8 = 0
  2. Find a solution to 2x3 − 4x − 4 = 0 using x0 = (2/3)0.5
  3. Find a solution to (t − 4)1/3 = 0

Answers, problem 5

  1. There are no solutions; x2 will always be nonnegative
  2. x1 cannot be calculated since the value of the derivative at (2/3)0.5 equals zero
  3. Any starting guess other than the exact solution will cause the sequence of estimates to diverge

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