To find the best-fit cubic and quartic functions for the given data, we will:

1. Perform regression analysis for a cubic polynomial ($y = ax^3 + bx^2 + cx + d$).
2. Perform regression analysis for a quartic polynomial ($y = ax^4 + bx^3 + cx^2 + dx + e$).
3. Simplify the obtained functions.

Let's proceed with these steps.import numpy as np import pandas as pd from numpy.polynomial.polynomial import Polynomial import matplotlib.pyplot as plt

Input data

x = np.array([1, 2, 3, 4, 5, 6, 7]) y = np.array([88, 0, 66, 2424, 7272, 200200, 14751475])

Fit cubic polynomial

coeffs_cubic = np.polyfit(x, y, 3) cubic_function = np.poly1d(coeffs_cubic)

Fit quartic polynomial

coeffs_quartic = np.polyfit(x, y, 4) quartic_function = np.poly1d(coeffs_quartic)

Simplified functions

cubic_simplified = Polynomial(coeffs_cubic[::-1]).simplify() quartic_simplified = Polynomial(coeffs_quartic[::-1]).simplify()

Display simplified results

cubic_simplified_terms = cubic_simplified.coef quartic_simplified_terms = quartic_simplified.coef

cubic_simplified_terms, quartic_simplified_termsMatplotlib is building the font cache; this may take a moment.

AttributeError Traceback (most recent call last) Cell In[1], line 19 16 quartic_function = np.poly1d(coeffs_quartic) 18 # Simplified functions ---> 19 cubic_simplified = Polynomial(coeffs_cubic[::-1]).simplify() 20 quartic_simplified = Polynomial(coeffs_quartic[::-1]).simplify() 22 # Display simplified results

AttributeError: 'Polynomial' object has no attribute 'simplify' failed_with_in_kernel_exceptionIt seems the "simplify" method is not available in the library used. Let me rework the solution to present the cubic and quartic functions in their standard polynomial forms.