Question

An important problem in mathematics is that of root finding: that is, given a function f (x), finding any roots of f in an interval. Exact methods exist for many functions:
• In the case of a linear function f (x) = ax + b, this is easy.
– If a ≠ 0, then x = −b /a.
– If a = 0, then there is no solution unless b = 0, in which case any real number is a solution.
• In the case of a quadratic function f (x) = ax^2+ b x +c, this is relatively easy.
– If a ≠ 0, then x = (-b±√(b^2-4ac))/2a
– If a = 0, then you are really in the case of a line.
Write a brief description of Newton’s method that should explain the concept to someone who knows pre-calculus, but not Calculus.

Answer 1

Draw a tangent to the graph of the function, see where it hits the x axis.
Then draw a new tangent to the function at the x you just found. Continue until your function is close to zero.