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Chapter 26 I am actually an expert
This was the first time in Qiao Yu’s life that he stood on the podium during a class.

Different perspectives give different feelings. It turns out that everything can be seen clearly, and no small movements can escape. It seems that he often thinks he is too smart, always thinking that the teacher can't see some small movements below.

In fact, it’s just a matter of whether you want to care or not.

Especially these little... no, these high school brothers and sisters, they don't know how to hide their emotions at all, what they are thinking is written directly on their faces, and they look easy to deal with...

Then Qiao Yu looked at Lang Jie who was standing beside the podium.

Sure enough, teachers are different. At least just looking at that emotionless face, it is impossible to tell what he is thinking at the moment.

After scanning the area, he finally focused his attention on the question.

"Let's take a look at this question first. Although it's a little simple, it's a very typical function equation analysis question. You should know at a glance that this question first requires considering the value of the function at a specific point to solve the equation...

At the same time, you can also verify and eliminate multiple possibilities by constructing specific functions. With these two points of knowledge, I believe everyone already knows how to solve this problem. "

"Ahem...Qiao Yu, just explain your ideas directly." Lang Jie couldn't stand it anymore and coughed twice.

"Oh."

Qiao Yu nodded and picked up the chalk resignedly: "The first step is to prove that f(x) is strictly monotonically increasing. We start with the question f(f(x))=f(x^2)+x and consider the derivatives of both sides with respect to x. We can assume that f'(x) represents the derivative of f(x). Obviously, when f′(x)=0, then 0=1, which is a contradiction. Therefore, f′(x)≠0..."

……

Five minutes later, Qiao Yu put down the chalk.

Ranjie next to him sighed. It turned out that this kid was really not easy to deal with.

Qiao Yu's attention was on the new students in the audience. The situation did not seem good. It seemed that only five students were watching his problem-solving process thoughtfully, including Ma Yufei and Lu Jia, with whom he had dealt before.

The expressions of most people clearly did not look like they understood what was said, especially many people were secretly glancing at Ranger who was standing on the other side of the podium...

That pure and innocent look didn't seem fake.

Not only did they not understand, they couldn't even tell whether their solution was correct!

Sure enough, Ma Yufei and Lu Jia who came to him were not isolated cases. The skills of these guys seemed to be not very good.

For a moment, Qiao Yu suddenly felt some sympathy for Langjie.

It is really too difficult to expect these people to participate in competitions after training, and also expect them to win medals and help the good guys earn some bonuses.

This also made Qiao Yu immediately realize why Lang Jie was so nice to him.

Athletes like him who don't need much training to participate in the competition seem to be a scarce resource and are in great demand. If schools have the choice, they will not send high school students who are obviously not up to the math standard to participate in the Olympiad training.

"Qiao Yu, you can go down first." Lang Jie nodded at Qiao Yu, then walked up to the podium.

When Qiao Yu walked down from the podium and returned to his seat with his back to the blackboard, Teacher Lan's voice was heard.

"Qiao Yu's solution is very clear, but he just glossed over some key steps, so you may not fully understand them. Let's look at the second question Qiao Yu analyzed. When considering possible function forms through the construction method, Qiao Yu directly substituted f(x)=x+1 into the original equation, which actually requires some calculations...

Similarly, when proving uniqueness, Qiao Yu used the method of contradiction to guide the possibility of analyzing function differences. The step he omitted here is actually the monotonicity of the derivative derived in the first question. After completing it, it is like this... In summary, to answer this question, you need to use a variety of mathematical tools such as differential foundation, function property analysis and construction method, and proof by contradiction. Today, I have prepared a question for you to think about... By the way, Qiao Yu, come with me to the office."

……

He didn't give Qiao Yu any time to stay in the classroom to discuss business with his classmates. After class, he took Qiao Yu back to his office.

However, Qiao Yu did not feel too regretful, as he had already realized that it was not an easy task to help these students explain the questions clearly.

For example, he just watched as Ranger re-examined the conclusion of the last example question, which was very obvious and could be thought of by anyone with a brain. The half of the blackboard he had left empty was filled up...

If it were him, his hands would be crippled just from writing on the blackboard after this class. Qiao Yu deeply felt that being a teacher is indeed not an easy job.

"Come here, move a stool and sit next to me." As soon as he entered the door, Lang Jie waved directly at Qiao Yu.

Qiao Yu obediently moved a stool over and sat down.

Ranger has already opened his laptop and opened the Overleaf interface.

"This is an online LaTeX editor. There is no Chinese version, but you should have no problem using it given your English level. I'll introduce the main commands to you. First, let's create a paragraph..."

Ranjie didn't waste any time. As soon as Qiao Yu sat next to him, he began to teach Qiao Yu how to use the LaTeX editor as he had promised on the phone yesterday.

The math teacher also once again witnessed Qiao Yu's talent.

I didn't see Qiao Yu taking any notes. He only had to do all the operations once and he would know them clearly.

Commands, formula editing, various lists, commonly used macro package operations and debugging can all be perfectly restored.

At first, Langjie thought that Qiao Yu's claim of knowing how to do it was a bit forced, but when he let Qiao Yu try it himself, his skillful operation even made him wonder if this kid had already had experience with it before and was just teasing him today.

Originally, Langjie had planned to have Qiao Yu come to school again tomorrow so that he could use the rest time to help this extremely talented student consolidate his knowledge, but now it seems unnecessary.

"Okay, that's about all you need to know. The definition of references is for writing papers, so you won't need it for now. Go back and try to do a few questions using the test system on the Xiaolibaba Mathematics Contest official website, then upload the answers and you should be able to fully understand it."

After seeing Qiao Yu finish his demonstration, Lang Jie said with infinite emotion.

After all, it took him at least a week to learn how to use this thing, and he's still not as proficient as Qiao Yu is now.

In the past, Lan Jie thought that the gap between him and those top students from Huaqing and Yanbei might not be that big. At most, he might have had bad luck, and the other party's tutors were very good and could provide more resources. But now he has completely lost this idea.

This world is really unfair. Many students seem to have excellent grades, but most of them have tried their best, while the best among them may just have studied casually. How the hell can you compare them?
You know, this guy skipped two days of classes two days ago and worked in an internet cafe to make money...

"It's really simple. If I had known this, I would have just found a tutorial and learned it myself yesterday." Qiao Yu nodded and stated a fact.

Lang Jie glanced at the little guy speechlessly, and reminded him again: "By the way, you will start a round of mock exams next Monday. You, Class 13, don't have to make up classes on the weekend. You should prepare first. The questions this time, except for mathematics, may be difficult."

Qiao Yu glanced at Lan Jie and suddenly realized that this math teacher seemed to be quite powerful. He could even arrange exams for the third grade. He didn't seem as pitiful as he imagined...

(End of this chapter)