需要帮助绘制和查找局部最大值和最小值在Python中使用渐近。第一部分可以工作，但不知道如何做其他部分

import numpy as np
import matplotlib.pyplot as plt

# 定义函数
def f(x):
    return np.sin(x) + 0.5 * x

# 绘制函数曲线
x = np.linspace(-10, 10, 1000)
y = f(x)
plt.plot(x, y)

# 使用渐近法查找局部最大值和最小值
epsilon = 1e-6  # 终止条件
max_iters = 1000  # 最大迭代次数

# 二分查找法
def bisection_search(a, b):
    for _ in range(max_iters):
        mid = (a + b) / 2
        if abs(f(mid + epsilon) - f(mid - epsilon)) < epsilon:
            return mid
        if f(mid - epsilon) > f(mid + epsilon):
            b = mid
        else:
            a = mid
    return (a + b) / 2

# 黄金分割法
def golden_section_search(a, b):
    rho = 2 - (1 + np.sqrt(5)) / 2  # 黄金分割比例
    x1 = a + rho * (b - a)
    x2 = b - rho * (b - a)
    for _ in range(max_iters):
        if f(x1) < f(x2):
            b = x2
            x2 = x1
            x1 = a + rho * (b - a)
        else:
            a = x1
            x1 = x2
            x2 = b - rho * (b - a)
    return (a + b) / 2

# 牛顿法
def newton_method(x0):
    x = x0
    for _ in range(max_iters):
        x -= f(x) / (2 * x + np.cos(x))  # 使用函数的一阶和二阶导数
    return x

# 查找局部最大值和最小值
local_max = bisection_search(-10, 10)
local_min = golden_section_search(-10, 10)
#local_min2 = newton_method(5)

# 绘制局部最大值和最小值点
plt.scatter(local_max, f(local_max), color='r', label='local max')
plt.scatter(local_min, f(local_min), color='g', label='local min')
#plt.scatter(local_min2, f(local_min2), color='b', label='local min 2')
plt.legend()

# 显示图像
plt.show()