在初四的数学与英语备考中，考研题目往往更具挑战性。以下是对这两科目的原创解答：
数学题解：
题目：若函数$f(x) = ax^2 + bx + c$在$x=1$时取得最小值，求$a, b, c$的关系。
解答：函数$f(x)$在$x=1$时取得最小值，意味着其导数$f'(x)$在$x=1$时为0。因此，我们有：
$$f'(x) = 2ax + b = 0$$
将$x=1$代入上式，得：
$$2a + b = 0$$
又因为$f(x)$在$x=1$时取得最小值，所以$a > 0$。结合以上条件，我们可以得出$a, b, c$的关系为：
$$2a + b = 0, \quad a > 0$$
英语题解：
题目：Read the following passage and answer the questions below.
"The world is changing rapidly, and with it, the way we live and work. Technology is advancing at an unprecedented rate, and it is transforming our lives in ways we could never have imagined. The internet has become an integral part of our daily lives, and it has revolutionized the way we communicate, access information, and conduct business. However, this rapid technological advancement also brings challenges. One of the most significant challenges is the digital divide, which refers to the gap between those who have access to digital technology and those who do not. This divide can have profound effects on individuals, communities, and societies as a whole."
Questions:
1. What is the main idea of the passage?
2. What is the digital divide?
解答：
1. The main idea of the passage is the impact of rapid technological advancement on our lives, focusing on the internet's role in transforming communication, information access, and business, and the challenges posed by the digital divide.
2. The digital divide refers to the gap between those who have access to digital technology and those who do not.
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