Methods2023 Exam 2 Section A · Q13CAS active1 mark

Newton's method algorithm with a For loop

The following algorithm applies Newton’s method using a For loop with 3 iterations.

Inputs: f(x), a function of x
        df(x), the derivative of f(x)
        x0, an initial estimate

Define newton(f(x), df(x), x0)
    For i from 1 to 3
        If df(x0) = 0 Then
            Return “Error: Division by zero”
        Else
            x0 ← x0 − f(x0) ÷ df(x0)
    EndFor
    Return x0

The Return value of the function newton(x³ + 3x − 3, 3x² + 3, 1) is closest to

1 mark

Inputs: f(x), a function of x df(x), the derivative of f(x) x0, an initial estimate Define newton(f(x), df(x), x0) For i from 1 to 3 If df(x0) = 0 Then Return “Error: Division by zero” Else x0 ← x0 − f(x0) ÷ df(x0) EndFor Return x0