Simple Scala program:

3. Problem: Finding Roots of Functions

def controlLoop[S]( state: S, cycle: Int, halt: (S, Int)=> Boolean, update: (S, Int)=>S): S = the final state

Newton devised an algorithm for approximating the roots of an arbitrary differential function, f, by iterating:

guess = guess - f(guess)/f'(guess)

Recall that f'(x) is the limit as delta approaches zero of:

(f(x + delta) f(x))/delta

Use Newton's method and your controlLoop to complete:

def solve(f: Double=>Double) = r where |f(r)| <= delta