Mathematics · University
One Newton iteration · formula reference
A single iteration is an approximation, not a guaranteed exact root. The derivative at x₀ must be nonzero.
Formula
A single iteration is an approximation, not a guaranteed exact root. The derivative at x₀ must be nonzero.
x₁ = x₀ − f(x₀)/f′(x₀)
Worked example
Apply one Newton iteration to f(x) = x² − 30, starting at x₀ = 3. Enter x₁. Round the final result to 4 decimal places if needed.
f′(x₀) = 6; x₁ = 3 − (-21)/(6).
6.5
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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