一、数学部分
1. 题目解析
题目:设函数\(f(x)=\frac{x^3-3x}{x^2-1}\),求\(f(x)\)的极值。
解析:
首先,求出函数\(f(x)\)的导数\(f'(x)\): $\(f'(x)=\frac{(3x^2-3)(x^2-1)-(x^3-3x)(2x)}{(x^2-1)^2}\)\( 化简得: \)\(f'(x)=\frac{3x^4-3x^2-3x^2+3-2x^4+6x^2}{(x^2-1)^2}\)\( \)\(f'(x)=\frac{x^4+6x^2-3}{(x^2-1)^2}\)$
令\(f'(x)=0\),解得\(x=\pm\sqrt{3}\)。
当\(x<-\sqrt{3}\)或\(x>\sqrt{3}\)时,\(f'(x)>0\),\(f(x)\)单调递增; 当\(-\sqrt{3}<x<\sqrt{3}\)时,\(f'(x)<0\),\(f(x)\)单调递减。
因此,\(f(x)\)在\(x=-\sqrt{3}\)处取得极大值,\(f(-\sqrt{3})=3\sqrt{3}\); 在\(x=\sqrt{3}\)处取得极小值,\(f(\sqrt{3})=-3\sqrt{3}\)。
2. 答案
答案:极大值为\(3\sqrt{3}\),极小值为\(-3\sqrt{3}\)。
二、英语部分
1. 题目解析
题目:阅读下列短文,然后回答问题。
短文:
The Internet has become an integral part of our lives. It has brought great convenience to us, but it also brings many problems. One of the most serious problems is cyberbullying.
Cyberbullying refers to the use of the Internet to harass, threaten, or intimidate others. It can take many forms, such as sending threatening messages, spreading rumors, or posting offensive comments. Cyberbullying can have serious consequences, including emotional distress, anxiety, and depression.
To combat cyberbullying, it is important to take several steps. First, we need to raise awareness about the issue. People need to understand that cyberbullying is a serious problem and that it can have serious consequences. Second, we need to educate people about how to protect themselves from cyberbullying. This includes teaching them how to block and report cyberbullies, as well as how to deal with cyberbullying situations. Finally, we need to take action against cyberbullies. This can involve reporting them to authorities or seeking legal advice.
问题:What are the consequences of cyberbullying?
解析:根据短文内容,我们可以得知,网络欺凌的后果包括情绪困扰、焦虑和抑郁。
2. 答案
答案:The consequences of cyberbullying include emotional distress, anxiety, and depression.
