From child prodigy to chief scientist

Including the test he took last night, he also lost several points on the function questions.

This prompted Xu Xiao to decisively focus on the lecture and put aside what she was doing.

Class 1 of Senior Three is the top class at Yucai High School. In the most recent mock exam, the class average score reached a terrifying 642 points.

And this is only their score at the beginning of their senior year of high school. If they have another year of review, their average score can be improved by about 20 points.

This means that the vast majority of them can easily exceed the score requirements of 985 universities and apply to top universities such as Tsinghua University and Yenching University.

As soon as class started, Xu Xiao felt how fast Sun Yifei was lecturing, and she was already finding it hard to keep up.

This feeling is completely different from when I was in the children's class. Although the teaching speed in the children's class is also fast, the difficulty of the knowledge is much lower.

It was quite unusual for Xu Xiao to jump from junior high to high school all at once, and to take such difficult classes.

In addition, because I am too short, my view was somewhat blocked by the people in front of me, so I had to move my chair and table.

However, as Xu Xiao gradually focused, the situation quickly improved.

When Xu Xiao is highly focused, she can maximize her brain's capabilities and will no longer easily lose focus.

This allowed him to make up for the gap in ability between himself and other students, and he was basically able to understand what Sun Yifei was saying.

Before we knew it, the 40-minute class was over.

However, Sun Yifei did not dismiss the get out of class immediately, but continued to write a problem on the blackboard.

"Think about this question after class, and I'll start explaining it in class."

In the senior year of high school, the course schedule is usually two consecutive classes for each subject, which allows for a more continuous learning experience.

In order to maximize the efficiency of class, Sun Yifei basically does not ask questions during class, and even makes use of the time after class.

The students were already used to this rhythm; some sat down to think about the problem, while others came up to discuss it with the teacher.

Xu Xiao also looked at the problem carefully, trying to find possible solutions.

"Given the function f(x) = e^x - ax - 1."

"(1): If f(x) ≥ 0 holds for any x ≥ 0, find the range of values ​​for the real number a;"

[At this point, I hope readers will remember our domain name: 10 ...

「（2）：当a=1时，证明对任意x＞0，有e^x-1＞xln（x+1）。」

In the past, if Xu Xiao encountered this kind of question, he would probably finish the first question and then not know where to start next.

However, after listening carefully to the lesson, he felt that he seemed to be able to solve the entire problem.

"The first question is a fairly standard problem concerning the constant validity of inequalities with parameters. We can first find the derivative, and then discuss the different cases..."

Having quickly completed the first question, Xu Xiao already had an idea for the second question.

"For the second question, constructing the difference function and then proving its normality by taking its derivative should be achievable. Alternatively, the bounding method could also work, but I'm not very familiar with that method yet, and I'm not sure if I could solve it..."

Compared to the constructor method, the bounding method is often simpler in its steps, but it also requires a higher level of ability from students.

If you can't cleverly construct the scaling mechanism, you might spend too much time solving the problem, or even get stuck.

To be on the safe side, Xu Xiao still prefers to use the constructor method, even if the steps are more complicated.

Just as Xu Xiao was about to continue writing, he noticed that Sun Yifei and several students on the podium seemed to be discussing on the blackboard how to solve the problem using the scaling method.

However, they blocked much of the blackboard, so Xu Xiao, who was in the last row, couldn't see it very clearly.

After a brief hesitation, Xu Xiao decided to walk towards the podium.

Seeing that the child in the back row had also come over, the others glanced at it curiously, but continued to discuss the question.

Upon reaching the podium, Xu Xiao finally saw all the content on the blackboard.

Just as he had guessed, they were indeed discussing using scaling to prove the second question.

However, the methods they have come up with so far all face various problems.

"To determine the sign of g'(x), we would need to find the second derivative of the function, which would make the problem too complicated."

"Could we use integral scaling?"

"No, the points are too advanced for the exam. Even if you get them right, you won't get any points."

"I was thinking of expanding on Taylor's material, but Taylor's material is also university level content."

Some students in the class had participated in high school math competitions and had a certain understanding of university-level mathematics.

However, the college entrance examination does not allow the use of knowledge beyond the syllabus to answer questions, which makes them feel like they have no way to use their strength.

Listening to their discussion, Xu Xiao suddenly had a flash of inspiration and immediately picked up a piece of chalk and started writing on the blackboard.

Xu Xiao's actions quickly attracted the attention of others.

They initially thought Xu Xiao was there to cause trouble, but after reading what Xu Xiao had written, they were all surprised.

"Holy crap...isn't this the Taylor expansion?"

"This kid can even do Taylor expansions? He's got some skills!"

"No wonder he came to our class to observe lessons; he's no ordinary kid."

Sun Yifei's face was also full of surprise. It seemed that the student recommended by Wang Ze did indeed have a strong talent for mathematics.

Xu Xiao was not affected by the praise from others and continued to write the process according to her own ideas.

In his previous life, Xu Xiao had studied advanced mathematics. Although he had forgotten much of the content, he still remembered classic formulas such as Taylor series expansions.

After watching Xu Xiao write for a while, Sun Yifei still said:

"Xu Xiao, there's nothing wrong with the Taylor series you wrote, but it's university-level math, while we need to use pure high school math to solve the problem."

Even if Xu Xiao were to use Taylor's method to prove it, he wouldn't get any points according to the college entrance examination standards.

"Teacher, I know. But if I can prove this inequality using high school methods, there shouldn't be any problem, right?"

"Prove it using high school methods...?"

This idea was something no one else had thought of, including Sun Yifei, who was also dumbfounded.

Using high school methods to prove university-level knowledge, and then applying that knowledge to high school problems, is indeed acceptable in principle.

While this method is not recommended, it is still an option to consider if no better method can be found.

Seeing that Sun Yifei did not deny it, Xu Xiao continued to deduce on the blackboard.