MediumCalculusca-022

Newton Method One Step

Problem

Take one Newton-Raphson step for the polynomial f(x) = sum(coeffs[i] * x^i), starting at x0:

x1 = x0 - f(x0) / f'(x0)

Return x1 as a float. Assume f'(x0) != 0.

Hint

Differentiate term by term, then subtract the ratio f / f' from x0.

case 1

in: [[-2,0,1],1]

expected: 1.5

case 2

in: [[-2,0,1],2]

expected: 1.5

case 3

in: [[-2,-1,0,1],2]

expected: 1.6363636363636365

case 4

in: [[0,0,1],3]

expected: 1.5

case 5

in: [[5,2],0]

expected: -2.5

Starter codePython

def newton_step(coeffs, x0):
    # Your code here
    pass

5 test cases · run your code against them in the editor