Please fill in the part of the code where stated #YOUR CODE HERE, written in python

Newton's method is often paired with a line search which finds the smallest non-negative integer k such that where Xn+1 = Xn-2-k f(X)/ f' (x) Implement this algorithm by shortening the step until the inequality is satisfied. def newtonis (f, a, b, tol-1e-1e): "Newton's method with a 1ine search""" x(a b) 2 history for i in range(100): fx, dfxf(x) history.append((x, if np.abs (fx)tol: fx)) break # YOUR CODE HERE raise NotImplementedError() return np.array(history) assert np.allclose (newtonls(tests[ 'monotonic_diverge'], e, 2)[-1], Newton's method is often paired with a line search which finds the smallest non-negative integer k such that where Xn+1 = Xn-2-k f(X)/ f' (x) Implement this algorithm by shortening the step until the inequality is satisfied. def newtonis (f, a, b, tol-1e-1e): "Newton's method with a 1ine search""" x(a b) 2 history for i in range(100): fx, dfxf(x) history.append((x, if np.abs (fx)tol: fx)) break # YOUR CODE HERE raise NotImplementedError() return np.array(history) assert np.allclose (newtonls(tests[ 'monotonic_diverge'], e, 2)[-1]