Hua Luogeng stared at the process of answering the second question on the blackboard. He couldn't help but nodded. He glanced at the sweaty Yu Hua, his eyes were full of approval, and he didn't make a sound to urge him to quickly solve the third question.
Now, in Hua Luogeng's mind, Yu Hua, who can finish the second question in one breath without stopping, has been rated as an outstanding mathematics seedling, with excellent mathematical talent, a very solid grasp of basic knowledge, and an extremely solid foundation.
However, the strange thing is why Yu Hua can do this question, but Zhao Anyuan, who has the first score, cannot?
After a short rest of twenty seconds, Yu Hua no longer hesitated and turned his eyes to the blackboard again, preparing to overcome the last difficulty in front of him in one go.
Among the whole function question, the most difficult one is the third question in front of me, which is also the content part that Yu Hua has not fully understood yet. He has calculated it more than ten times and gets stuck here every time.
Take a deep breath, adjust your posture, hold the chalk in your hand, and start writing again.
(3)
f'(x)=e??+txe?-e?=e??[1+tx-e(1-t)x]≤e......
When t≤1/2 and x>0, f'(x)=e??[1+tx-e(1-t)x]≤e...
1+x-e?＜0, there is also 1+x/2-e x/2＜0, so f＇(x)＜0, so the function f(x) decreases monotonically within (0,+∞);
When 1/21,
After writing the mathematical formulas and steps here, Yu Hua stopped, frowning, and stared at the blackboard. He found that he still seemed unable to solve the third problem.
Seeing Yu Hua pause, everyone in the classroom followed suit. Their breaths froze, and all their eyes focused on Yu Hua.
Can’t figure it out?
Fang Yu's eyes were a little disappointed, and she thought silently in her heart. She didn't have any jealousy, only regret. Failure always makes people feel that something is missing.
Come on, Yu Hua!
Zhou Yuan silently clenched his right hand, and deep in his heart, he cheered for his classmate who was as ambitious as the sky.
An invisible and solemn atmosphere permeated the surroundings.
silence.
Deathly silence.
Time passed little by little, and after half a minute, Yu Hua, who was facing the blackboard, shook his head gently, sighed, and was about to put down the chalk and apologize to Hua Luogeng.
"Take x=1, when t≥1, it is inconsistent with what is known." At this moment, a calm and discerning voice came over, which was a reminder from Mr. Hua Luogeng.
The words were smooth and clear, reaching Yu Hua's ears.
contradiction?
Contradictory to what is known?
Suddenly, Yu Hua, who was about to give up, suddenly froze on the spot. His mind seemed to explode like an explosion, and he went blank. Then, his whole person seemed to have broken through the shackles and understood the situation in the third question. Countless mathematics
Symbols and formulas circulate and are arranged according to extremely strict rules.
He figured it out.
"Squeak!" A sharp and harsh friction sound came out, and the chalk scratched on the surface of the blackboard, outlining beautiful and elegant mathematical symbols.
Yu Hua seemed to be possessed, his eyes were fixed on the blackboard, and he was writing extremely fast with his right hand.
"Let h(x)=1+tx-e(1-t)?, then h(0)=0, h'(x)=(1-t)［t/1-t-e(1-t)x
], when 0＜x＜1/1-t Ln t/1-t, h'(x)＞0, so h(x) is within (0,1/1-t Ln t/1-t)
Monotonically decreasing, so h(x)>h(0)=0, at this time f'(x)>0, so the function f(x)>f(0)=0, which is inconsistent with the question hypothesis. In summary, when and
Only when t≤1/2, the function f(x) is a decreasing function within (0,+∞).”
His forehead was covered with sweat. Yu Hua became more and more excited as he wrote. He could only see the blackboard and mathematical characters and nothing else. He even read out the words while writing.
After a minute, the sound of chalk writing on the blackboard disappeared.
There was silence in the classroom.
"Bah bang bang!" The next second, applause suddenly burst out in the classroom. This was the applause from all the students in the Science Class 1, and it was not for anything else, but for Yu Hua who composed the question.
Yu Hua completed this extremely difficult function question almost by himself.
"This is a top-notch mathematics seedling." Hua Luogeng smiled with his face and applauded Yu Hua on the podium with both hands. He was very impressed in his heart and his evaluation reached a new level.
He wiped the sweat from his forehead with his dusty right hand and looked at the blackboard. He stood still and an imperceptible arc appeared at the corner of his mouth. At this moment, Yu Hua, who was enjoying the applause of his classmates, felt an overwhelming sense of accomplishment. In front of Hua Luogeng
After solving this problem in front of the whole class, this feeling is simply more refreshing than drinking a bottle of Bingkuoluo in the dog days of summer.
When you get rich, you must try Coca-Cola in 1937.
"Sir, Yu Hua figured it out. Thank you for your advice." Yu Hua was not too proud. He put down the chalk, turned around, faced Hua Luogeng, and said respectfully.
Hua Luogeng smiled and said: "You don't need to thank me. If you want to thank me, just thank yourself. It's easy to understand. That's right. Let's go down first."
"yes."
Yu Hua respectfully said goodbye to Hua Luogeng, turned around and walked off the podium, and felt the eyes of a famous classmate looking directly at him. When passing by the first row, Zhao Anyuan, Fang Yu, Li Fan and other top students gave a thumbs up in unison.
Yu Hua grinned at everyone and returned to his seat to sit down under everyone's gaze.
"Awesome! You are so awesome! You really shocked the whole audience today and shocked everyone." After Yu Hua just sat down, Zhou Yuan gave a thumbs up and praised quietly.
"Class, class." Hearing Zhou Yuan's compliment, Yu Hua smiled and had to say that this feeling was really comfortable.
On the podium, Hua Luogeng returned to the center of the podium and said to everyone: "Yu Hua's answer is very correct. Have you understood it?"
Do you understand?
Except for a few top students in the first row who could barely understand, everyone else blinked in confusion.
Although I watched Yu Hua's problem-solving process, the essence of the problem in front of me has not changed at all, and I still cannot understand it.
Can you understand it after reading it once?
joke.
Sir, you really admire our intelligence.
"Copy it down if you don't understand it, and study it after class. I gave a total of three function questions, easy, normal, and medium in difficulty. You all raised your hands enthusiastically for the first question, only a few people raised their hands for the second question, and only a few people raised their hands for the third question.
Only Yu Hua raised his hand. This is where there are so many changes in functions. Functions include derivatives, and derivatives are derivatives. From derivatives to higher, there are differentials and integrals. If you want to get into university, you can start a scientific research career in the future.
, be sure to learn the basics of functions.”
Hua Luogeng felt the helpless looks of everyone, smiled, and slowly explained: "Do you understand?"
Function is one of the basic knowledge. Hua Luogeng tested everyone through three questions, with only one purpose, so that they can truly understand the importance and significance of arithmetic.
If you want to engage in science and scientific work, you cannot do without a solid foundation in mathematics.
Don’t know how to calculate?
How to obtain parameters such as projectile trajectory and velocity variables?
How does an airplane fly at high speed?
How to obtain the gas flow velocity and change data on the fuselage surface?
If you don't know how to calculate, the path of scientific research will be really difficult.
"I understand, thank you for your teaching." All the students stood up and said respectfully.
Looking at Hua Luogeng on the podium, Yu Hua's eyes were filled with respect.
"Boom! Boom! Boom!" The next moment, the bell that represented the end of the first class rang. It was low and distant, with penetrating power, and spread throughout the Fourth Middle School.
Hearing the bell ringing outside the classroom, Hua Luogeng walked down the platform with a smile and bowed to a student from Class 1 of Neo-Confucianism and left the classroom.
The first lesson of the semester is over.
Today, Peking No. 4 Middle School not only welcomed Hua Luogeng, a professor of mathematics from National Tsinghua University, but also the literature classes next door welcomed Chen Yinke, Wen Yiduo, Feng Youlan and other nationally famous National Tsinghua professors to personally teach the first lesson of the semester.