"Oh? Classmate Anyuan, have you figured it out yet?" Seeing this, Hua Luogeng was slightly surprised and looked at Zhao Anyuan, who was sitting in the first place, with some expectation.
expect.
If Zhao Anyuan can really solve the problem so quickly, it means that the child in front of him has excellent mathematical talent and is a top-notch mathematical talent.
As for Yu Hua who has not yet come down from the podium?
He can only be called a budding mathematician, not a top performer.
Zhao Anyuan, who was attracting the attention of everyone, stood up without leaving his seat. His face was serious, his eyes were fixed on Hua Luogeng, and he said respectfully: "Sir, no, can you give us 10 minutes?"
Ten minutes.
The function question on the blackboard was too complicated, and the difficulty suddenly dropped from medium to lower. Don’t finish it immediately. Even Zhao Anyuan, who ranked first in mathematics, could not analyze his ideas for a while. Five minutes of thinking time was a bit too short.
Zhao Anyuan's words spread throughout the classroom, and all the numb students breathed a sigh of relief. They really thought Zhao Anyuan had solved the problem.
"cannot."
Hua Luogeng shook his head and refused Zhao Anyuan's request without hesitation, reminding: "This question is not difficult, it just looks complicated. Please review it carefully."
Not too difficult?
Only you, professor, can say that.
Zhao Anyuan, who was rejected, looked helpless. He sat down properly and turned his eyes to the blackboard again, studying it carefully.
Fang Yu, Li Fan, and all the students stared at the question and thought about it, but they couldn't figure it out.
Yu Hua, standing on the right side of the podium, silently stared at the question in front of him. Various knowledge points about functions kept emerging in his mind. Formulas kept appearing one after another to form the corresponding steps for the answer. However, if he could not deduce a few steps, he could no longer deduce it.
Go down.
Unable to calculate means the steps and data are wrong.
Start over.
The easiest part of this function question is the first question. The difficulty of the second and third questions increases in sequence, showing a linear increasing trend.
It has to be said that as a professor at National Tsinghua University, Hua Luogeng's strength is really terrifying. A random question is equivalent to the final question of the college entrance examination and the final question of the simulation paper of the famous school in later generations.
The most important thing is that it was not the professor who created Hua Luogeng, but Hua Luogeng who created the professor.
Time passes minute by minute.
After more than three minutes, the classroom was silent, and the atmosphere was eerily quiet.
No idea.
Still no idea.
Zhao Anyuan's face was serious, Fang Yu's brows were furrowed, and Li Fan even had a thin layer of sweat on his forehead. A student from Class 1 of Neo-Confucianism was almost racking his brains. As the top and best high school student in the country,
At this moment, he is as stupid as a three-year-old child.
The time comes to the fourth minute.
"Sir, I have an idea, but..." At this time, Yu Hua, who was standing next to the podium, raised his right hand and hesitated to speak. After more than ten attempts, he finally had an idea.
However, there is a problem.
He could solve the problem, but not completely.
"Come up if you have an idea. It doesn't matter if you are wrong." Hua Luogeng, who had been waiting for a long time, heard Yu Hua's voice, and his eyes suddenly lit up, and he encouraged him.
Hua Luogeng thought that no one would have an idea for the question he asked within five minutes. Unexpectedly, Yu Hua, the student he met eight days ago, really had some talent in mathematics.
As expected, he was not disappointed. He was a good mathematical talent, not bad.
Hearing Hua Luogeng's encouragement, Yu Hua took a deep breath, gained confidence in himself, stepped forward and picked up the chalk again, turned around, and faced the blackboard.
At this moment, Yu Hua could clearly feel the focused gazes from the whole class.
The focus of the audience!
With a calm face and a calm demeanor, Yu Hua stared ahead and wrote with his right hand.
"Squeak!" The chalk rubbed against the blackboard, leaving a trail of countless white powders and a subtle but sharp friction sound.
untie:
(1) When t=0, f(x)=x-e?+1, f＇(x)=1-e?.
When x＜0, f′(x)＞0; when x＞0, f′(x)＜0, so f(x) increases monotonically in (-∞,0), and increases monotonically in (0,+∞
) decreases monotonically.
∴f(x)???=f(0)=0.
After writing the answer to the first question, Yu Hua paused for a moment and closed his eyes. The experience he had calculated dozens of times in his mind told him that the answer to the first question was correct.
In the audience, Zhao Anyuan, Fang Yu, Li Fan and other top students were stunned when they saw Yu Hua give the answer to the first question. They quickly deduced in their minds. After a few seconds, they were a little confused.
The answer is correct.
Looking at the solution to the first question and the answer on the blackboard, Hua Luogeng nodded and looked at Yu Hua in front of him, with a hint of expectation in his eyes.
Rest for ten seconds, open your eyes again, and resume writing.
Next, there is the second question, which is more than several times more difficult. This question extremely tests whether the students' foundation is solid.
Watching Yu Hua start writing again, all the students in the audience were holding their breath, not even daring to take a breath. Fang Yu's eyes fell on the blackboard, and her right hand turned the pencil faster and faster. She was a little nervous and expectant.
(2) From f(x)=1, we get xe??=e?, that is, x=e??1?? ?>0, so the original equation has no negative real roots, so lnx/x=1-t,
Let g(x)=lnx/x, g′(x)=1-lnx/x2, when 0＜x＜e, f＇(x)＞0; when x＞e, f＇(x)＜
0;
Therefore, the function f(x) increases monotonically within (0,e) and decreases monotonically within (e,+∞), then g(x)???=g(e)=1/e,
Therefore, the value range of function g(x) is (-∞,1/e],
The equation f(x)=1 has no positive real roots, that is, 1-t>1/e. To sum up, when t<1-1/e, the equation f(x)=1 has no real roots.
The time has passed three minutes.
As soon as he finished writing, Yu Hua's forehead was covered with sweat, and his brain was dizzy, showing a hint of exhaustion. His head was working at full capacity, which consumed a lot of energy and physical strength. Unfortunately, he ate a piece of chocolate and steamed buns before class.
After finishing writing, Yu Hua looked up at the blackboard full of mathematical characters, and let out a long breath of suffocation in his chest. He felt extremely comfortable. The mathematical formulas and problem-solving experience told him that the second question was still correct.
Comfortable.
At this moment, Yu Hua felt refreshed.
At this time, there was silence in the audience. The students were no longer dumbfounded. Instead, they were holding pens and scratch paper in their hands and kept copying the answer to the second question written by Yu Hua. As for whether it was correct or not, it was not yet known.
No matter how many there are, if I copy them now, even if they are wrong, they are still worthy of reference.
When doing math problems, the most important thing is the idea of solving the problem.
If you have an idea, everything will be easy to do.
If you look confused after reading the question, it means you will lose more than ten points.
"I actually solved it." The girl Fang Yu copied very quickly and understood while copying. With her strong logical thinking, she quickly understood that the steps and answers to Yu Hua's second question were very close to each other. She glanced at the podium.
Yu Hua, who was sitting on the bed, murmured secretly in his heart, feeling that he couldn't explain what he was talking about.