Newton's Method: Quiz

Problem 5

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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