Volume 1: Student Life Chapter 41: All Fur
Chen Zhou looked at the set of papers and a math reference book, weighed the pros and cons and decided to do the papers.
The time spent on a test paper is easier to control. It is not like studying in a reference book, where there are too many questions. If you immerse yourself in it, you probably won't wake up until tomorrow morning when the effect of the drug wears off.
If that's the case, then tomorrow's class will be ruined!
So Chen Zhou threw the reference book aside, opened the test paper, and prepared to start working.
"Um?"
A piece of draft paper fell out of the reference book. Chen Zhou took it and looked at it, then he remembered the notes he had made in the afternoon.
The contents on this draft paper were exactly the two names he wrote in the afternoon.
Lagrange's mean value theorem.
Cauchy's mean value theorem.
Chen Zhou was very sure that he did not know these two people, and unless it was necessary, he did not really want to know them.
Just like he didn't want to know the talkative Confucius.
When Chen Zhou was in Chinese class, he once thought about a question: Why did Confucius love to talk so much?
Also, not only did Confucius love to talk, but someone also compiled his words into "The Analects of Confucius".
It would be fine if you just sorted it out, but you still have to memorize it when you go to school...
Well, there are Newton, Vieta, Ohm, Coulomb, Archimedes, and so on.
Chen Zhou picked up his phone, opened the Baidu search input box, typed in "Lagrange's mean value theorem", and clicked Baidu search.
Looking at more than 2 million pieces of related information, Chen Zhou couldn't help but feel his scalp tingling.
He didn't believe what the system said. How could a hidden task simply require understanding these theorems?
You know, he persisted for 50 days to get the task of obtaining the collection of wrong questions!
Chen Zhou clicked on Baisou Encyclopedia, intending to first look at this person's theorem and then slowly figure out the system's intentions.
"Lagrange's mean value theorem, also known as Lagrange's theorem, is one of the basic theorems in differential calculus. French mathematician Lagrange proposed this theorem in Chapter 6 of his book "Theory of Analytical Functions" in 1797 and gave a preliminary proof. Therefore, people named this theorem Lagrange's mean value theorem..."
"…Theorem states that if a function f(x) satisfies: (1) it is continuous on the closed interval [a, b]; (2) it is differentiable on the open interval (a, b); then there is at least one point ε (a＜ε＜b) on the open interval (a, b) such that the equation f(b)-f(a)=f′(ε)(b-a) holds…"
"What is differential calculus? Is it mathematics? But this formula seems familiar..."
Chen Zhou quickly finished reading the entire Baisou Encyclopedia. He understood and remembered what the Lagrange mean value theorem was, and even felt somewhat familiar with it.
Chen Zhou took a quick glance and saw the small paper thrown aside. He immediately exclaimed, "Isn't this the function question that is often asked in exams?"
Chen Zhou thought about the timing and conditions that triggered the hidden task at that time, all because he longed for a simpler way to solve the function problem.
After figuring this out, he returned to the Baidu search input box and began searching for "Application of Lagrange's Mean Value Theorem in College Entrance Examination Mathematics".
Chen Zhou clicked on a search message, which was full of theorems and corollaries of Lagrange's mean value theorem and examples of its application in solving practical problems.
Chen Zhou was not in a hurry to read the contents, but instead focused on the opening paragraph.
The general content is that current high school textbooks have added a lot of knowledge about derivatives, and there are many questions in the college entrance examination that are based on advanced mathematics. If you can appropriately apply the ideas of advanced mathematics and the basic ideas of constructors to derivative problems, and understand some basic applications of Lagrange's mean value theorem in advance, it will be of great help in solving problems about functions, inequalities, etc.
After reading this, Chen Zhou was thinking: "Isn't Lagrange's mean value theorem a basic theorem in differential calculus? Why is it in advanced mathematics? Also, isn't this advanced mathematics something you have to learn in college?"
Chen Zhou couldn't figure it out, and he felt a headache: "Could it be that the system is messing with me again? I haven't read the Cauchy Mean Value Theorem yet. Is it so complicated?"
Chen Zhou sighed lightly, blaming himself for getting too high and drinking it all in one gulp, which was indeed not something a human should do.
If you can’t sleep now, then study!
Chen Zhou continued reading the article.
Under the effect of the psychic potion, Chen Zhou soon immersed himself in that wonderful state of learning again.
Lagrange's mean value theorem is not a very profound theorem, and it does have very clever applications to function problems in high school mathematics.
Unconsciously, Chen Zhou memorized several common techniques of this theorem.
After finishing an article, Chen Zhou felt a little unsatisfied. He felt that these were real mathematical knowledge , and what he usually learned were just nonsense.
There is such a simple and convenient theorem that can be used, why not teach it?
Chen Zhou took the small test paper, found a function question from it, and was eager to try it out.
Just do it!
Chen Zhou quickly looked over the question.
Prove that when x∈［1，＋∞）, ln（1＋1/x）^x≥ln2.
The question is not difficult, but according to the previous thinking, it will be troublesome.
So, after moving one side to the other, constructing the function, and taking the derivative, Chen Zhou substituted the Lagrange mean value theorem for calculation.
It can be directly obtained that f(x) is monotonically increasing on x∈［1，＋∞）, so f(x)≥f(1), that is, the above inequality holds.
"Fuck... this is much easier... "
After Chen Zhou reviewed his problem-solving steps again, he realized the usefulness of this theorem.
Suddenly, Chen Zhou's eyes became hot as he looked at the Lagrange mean value theorem on his phone.
Chen Zhou pressed the phone quickly, constantly switching between the search box and the search content.
In immersive mode, Chen Zhou studied at the highest efficiency and absorbed the essence of Lagrange.
He fell into that wonderful state again!
Before we knew it, the sky had turned pale.
It was not until Chen Zhou's alarm clock rang that he was called back from the ocean of knowledge.
At this moment, the effect of the medicine had almost worn off, and Chen Zhou's eyes were already covered with big bags.
Looking at the alarm clock that was ringing, Chen Zhou couldn't help but yawned.
After wiping away the tears that overflowed from his eyes due to yawning, he reached out to turn off the alarm clock.
In fact, Chen Zhou didn’t feel tired. There was even satisfaction and joy on his face.
The more he studied Lagrange's mean value theorem, the more he was impressed by the profoundness of mathematics.
It turns out that advanced mathematics is just a textbook for most college students. Lagrange's mean value theorem is just a little knowledge point in advanced mathematics and just a drop in the ocean of differential calculus.
However, differential calculus is only a branch of the vast mathematics.
"fur……"
Chen Zhou realized that what he had learned was just the basics.
No, even the advanced mathematics you learn in college is just the basics.
After washing his face and packing up his books, Chen Zhou went out.
At Maochang High School, it is better not to ask for leave casually.
Even so, he was already .
However, just in case, Chen Zhou poured another can of psychiatric medicine into the thermos.
