Numerical methods: Newton's method: watch it solved step by step

Find a root with tangent lines: each guess is the last tangent's crossing of the axis. A convergence table and graph. Level: University. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: Newton: x^3 - x - 1, start 1.5, 4 iterations

1. Understanding the problem. We want a root: a value of x where f(x) = 0. Newton's method starts from a guess and uses the tangent line to jump to a much better one.
2. The derivative gives the slope. The tangent at x_n has slope f'(x_n). Differentiate f (the Lab's engine does it exactly).
3. Newton's formula. Follow the tangent down to where it crosses the x-axis. That crossing point is the next guess.
4. The first iteration. Put the starting guess into the formula.
5. Keep going. Each row starts where the last ended. Watch the number of correct digits roughly double every step: that is the speed of Newton's method.
6. Check. Put the answer back into f: it should be almost zero.

Answer: x ≈ 1.32471796 after 4 iterations (f(x) ≈ 0)

Practise numerical methods: newton's method with problems the Lab marks for you.