annoying_function.js

const newton = (x0, fn, derivative) => {

    const estimates = [x0]

    let next, last
    while ( estimates.slice(-1).pop() > 0.09 ){
        
        last = estimates.slice(-1)[0]

        next = last - (fn(last)/derivative(last))
        estimates.push(next)

    }

    return estimates.slice(-1)[0]

}

const f = (x) => {
    return Math.pow( Math.E, ( -1/( Math.pow(x,2) ) ) )
}

const df = (x) => {
    return ( 1/Math.pow(x,3) )*( 2*( Math.pow( Math.E, ( -1/Math.pow(x,2) ) ) ) )
}

console.log(newton(0.1, f, df))