## 3. Differentiation ##

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(-5, 6, 110)
y = -2*x + 3
plt.plot(x, y)

## 6. Power Rule ##

x = 2
slope_one = 5*x**4
x2 = 0
slope_two = 9*x2**8

## 7. Linearity Of Differentiation ##

x = 1
slope_three = 5*x**4 -1
x2 = 2
slope_four = 3*x2**2 -2*x2

## 8. Practicing Finding Extreme Values ##

rel_min = [2/3]
rel_max = [0]

f_prime_onethird = 3*((1/3)**2) - 2*(1/3)
f_prime_threethirds = 3*(1**2) - 2*1
p_prime_minusone = 3*(-1**2) - 2*(-1)