'''Test function #1 in Exercise 8.8'''
def f1(x):
  return x**8 - 8*x**7 + 28*x**6 - 56*x**5 + 70*x**4 - \
         56*x**3 +28*x**2 - 8*x +1

'''Derivative of test function #1 in Exercise 8.8'''
def df1(x):
  return 8*x**7 - 7*8*x**6 + 6*28*x**5 - 5*56*x**4 + 4*70*x**3 \
        - 3*56*x**2 +2*28*x - 8

'''Test function #2 in Exercise 8.8'''
def f2(x):
  return (x-1)**8

'''Derivative of test function #2 in Exercise 8.8'''
def df2(x):
  return 8*(x-1)**7