my scientific age

Chapter 38 Refreshing
"Oh? Classmate An Yuan, have you come up with it already?" Hua Luogeng was slightly surprised when he saw this, and turned his eyes to Zhao Anyuan, who was sitting in the first place, with some anticipation.

look forward to.

If Zhao Anyuan can really solve the problem so quickly, it means that the child in front of him has an excellent mathematical talent and is a superb mathematical seedling.

As for Yu Hua, who has not yet stepped down from the podium?
It can only be called a mathematical seedling, not a superb one.

The much-anticipated Zhao Anyuan stood up and did not leave his seat. With a serious face, he stared at Hua Luogeng and said respectfully, "Mr. Hui, no, can you give us 10 minutes."

10 minutes.

The function problem on the blackboard was too complicated, and the difficulty level went from below the middle level to the full level. Rao Zhao Anyuan, who scored first in mathematics, didn't have a solution for a while, and 5 minutes of thinking time was a bit too short.

Zhao Anyuan's words spread throughout the classroom, and all the students with numb scalps breathed a sigh of relief. They really thought that Zhao Anyuan had solved it.

"No."

Hua Luogeng shook his head, refused Zhao Anyuan's request without hesitation, and reminded; "This question is not very difficult, but it looks complicated. You should review the question carefully."

Is it not difficult?
Only a professor can say that.

Zhao Anyuan, who was rejected, was helpless, he sat down according to the rules, his eyes turned to the blackboard again, and he studied 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, who was standing on the right side of the podium, silently stared at the topic in front of him. Various knowledge points about functions kept appearing in his mind, and formulas kept appearing to form the corresponding answer steps. go down.

Unable to calculate, means wrong steps and data.

Again.

The easiest part of this function question is the first sub-question, the second and third sub-questions increase in difficulty in order, showing a linear increasing trend.

I have to say that Hua Luogeng, a professor of National Tsinghua University, has such a terrifying strength that a random question is equivalent to the finale of the college entrance examination and the finale of the simulation paper of a famous school.

The most important thing is that it is not the professor who makes Hua Luogeng, but Hua Luogeng who makes the professor.

Time passed by minute by minute.

After more than three minutes, the classroom was silent and the atmosphere was terrifyingly quiet.

No idea.

Still no idea.

Zhao Anyuan's face was full of seriousness, Fang Yu's brows were wrinkled, and a thin layer of sweat even oozes out of Li Fan's forehead. A student from the first class of name and science almost racked 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 came to the 4th minute.

"Sir, I have an idea, but..." At this time, Yu Hua, who was standing beside the podium, raised his right hand and hesitated. After more than ten attempts, he finally had an idea.

However, there is a problem.

He could solve this problem, but not completely.

"Come up if you have an idea, it's okay to be wrong." Hua Luogeng, who had been waiting for a long time, heard Yu Hua's voice, his eyes suddenly lit up, and he encouraged him.

Hua Luogeng thought that no one could have an idea within 5 minutes of the problem he posed. Unexpectedly, the student Yu Hua he met eight days ago was really talented in mathematics.

Sure enough, it didn't disappoint him, it's a good math seedling, not bad.

Hearing Hua Luogeng's encouragement, Yu Hua took a deep breath, gave himself confidence, took a step forward and picked up the chalk again, turned around and faced the blackboard.

At this moment, Yu Hua could clearly feel the focused gaze from the whole class.

The focus of the audience!

With a calm expression and a calm demeanor, Yu Hua stared straight ahead, writing with his right hand.

"Squeak!" The chalk rubbed against the blackboard, leaving a trail of countless white powders, and a fine and sharp rubbing sound came out.

solution:
(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 in (0, +∞) ) is monotonically decreasing.

∴f(x)=f(0)=0.

After writing the answer to the first sub-question, Yu Hua paused for a while, closed his eyes, and the experience in his mind that he had calculated over a dozen times told him that the first sub-question was correct.

In the audience, Zhao Anyuan, Fang Yu, Li Fan, and other top-ranking students were stunned when they saw Yu Hua's answer to the first sub-question.

The answer is correct.

Looking at the solution and answer to the first sub-question on the blackboard, Hua Luogeng nodded and looked at Yu Hua in front of him with a hint of anticipation in his eyes.

After resting for ten seconds, he opened his eyes again and resumed writing.

Next, the second sub-question with increasing difficulty several times, this sub-question extremely tests whether students have a solid foundation.

Seeing Yu Hua start writing again, all the students in the audience held their breaths and didn't even dare to breathe. Fang Yu's pair of phoenix eyes fell on the blackboard, and the speed of turning the pencil in her right hand was getting faster and faster. She was a little nervous and looking forward to it.

(2) From f(x)=1, xe=e, that is, x=e > 0, so the original equation has no negative real root, so lnx/x=1-t, let g(x)=lnx/x , g'(x)=1-lnx/x, when 0<x<e, f'(x)>0; when x>e, f'(x)<0;

So the function f(x) increases monotonically in (0, e) and decreases monotonically in (e, +∞), then g(x)=g(e)=1/e,

So the value range of the 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.

Time, 3 minutes have passed.

Writing down, Yu Hua's forehead was full of sweat, and his brain was dizzy, showing a hint of exhaustion. The full load of his head consumed a lot of energy and physical strength, and he ate a piece of chocolate and steamed buns before class.

After writing, Yu Hua looked up at the blackboard full of mathematical characters, and let out a long mouthful of stasis in his chest. He felt extremely comfortable. The mathematical formulas and experience in doing the questions told him that the second sub-question was still correct.

Comfortable.

At this moment, Yu Hua only felt refreshed.

At this time, the audience was silent, and the students were no longer stunned. Instead, they held signature pens and scratch paper, and kept copying the answer to the second sub-question written by Yu Hua. As for whether it was correct or not, I don't know for the time being.

No matter how much, I will copy it now, even if it is wrong, it is worth learning and reference.

When doing math problems, the most important thing is to solve the problem.

With an idea, everything is easy to do.

If you are confused after reading the question, yes, it means that you will lose ten points.

"It turned out to be a real solution." The girl Fang Yu copied very fast, and understood while copying. With strong logical thinking, she quickly understood that the steps and answers of Yu Hua's second sub-question were inseparable. Yu Hua, who was on top, muttered inwardly, with a feeling of inexhaustible words and incomprehension.

Seems like a fake second.

(End of this chapter)