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Project: MAT 1630
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Kernel: Python 3 (system-wide)

Cubic Polynomial Derivatives

Let f(x)=ax3+bx2+cx+df(x)=ax^3+bx^2+cx+d be a cubic polynomial. Then the derivative of f(x)f(x) is given by f′(x)=3ax2+2bx+cf'(x)=3ax^2+2bx+c. We can now use this formula and list comprehensions to plot both f(x)f(x) and f′(x)f'(x) in a single plot on the inteval [−10,10][-10,10] using at least 10001000 sample points.

import matplotlib.pyplot as plt

def cube_deriv(a,b,c,d):
    x = [-10+20*i/1000 for i in range(1001)]
    y_f = [a*n**3+b*n**2+c*n+d for n in x]
    y_f_prime = [3*a*n**2+2*b*n+c for n in x]
    plt.scatter(x,y_f,color='blue',label="$f(x)$")
    plt.scatter(x,y_f_prime,color='red',label="$f'(x)$")
    plt.title("Plot of $f(x)$ and $f'(x)$.")
    plt.legend()
    plt.show()

cube_deriv(3,1,-2,5)
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