y=x^2的图像的切线python

在Python中，我们可以使用matplotlib库绘制y = x^2的图像，并通过numpy计算特定点的切线。首先，我们需要导入必要的库：

import numpy as np
import matplotlib.pyplot as plt
from sympy import symbols, diff

# 定义变量x
x = symbols('x')

# 函数y = x^2
y = x**2

# 计算函数的一阶导数，即斜率(切线的斜率)
dy_dx = diff(y, x)

def tangent_line(x_value):
    slope = dy_dx.subs(x, x_value)
    return slope, y.subs(x, x_value)

# 创建x的范围
x_values = np.linspace(-10, 10, 400)

# 计算并存储每个x值处的切线信息
lines_info = [(x_i, tangent_line(x_i)[0], tangent_line(x_i)[1]) for x_i in x_values]

# 绘制原函数图和切线
plt.figure(figsize=(8,6))
plt.plot(x_values, x_values**2, label='y=x^2', color='blue')
for line_info in lines_info:
    x_intercept, slope, y_intercept = line_info
    plt.plot([x_intercept, x_intercept + 1], [y_intercept, slope * (x_intercept + 1) + y_intercept], 'r-o', linewidth=0.5)

# 添加标签和标题
plt.xlabel('x')
plt.ylabel('y')
plt.title('y = x^2 的切线')
plt.legend()
plt.grid(True)
plt.show()