my scientific age

37 5 minutes

"What's the solution to this question?" After writing the chalk, Hua Luogeng turned sideways and turned to look at the crowd.

Everyone in the classroom stared at the blackboard and carefully reviewed the problem. This function problem, which was based on the modern definition of functions but had never been seen before, trapped many people.

I have to say that Hua Luogeng is indeed a master of mathematics in this era.

After five seconds, seven or eight people in the class raised their right hands. Most of the boys sitting in the front row, Yu Hua, also raised their right hands. After a short thought, he had an idea to solve the problem.

Hua Luogeng pointed to Zhao Anyuan, who was sitting in the first row, and motioned to come on stage: "This classmate, come and answer."

Zhao Anyuan did not hesitate at all. As the strongest man in the Neo-Confucian class, he did his part to step onto the podium. Under the watchful eyes of Hua Luogeng and a group of students, he picked up chalk and solved the problem.

Solution: ∵y=bx+1>1, if A∩B has only a subset, then A∩B=, ∴a≤1, the value range is (-∞, 1)

"Sir, An Yuan has solved it." After Zhao Anyuan finished writing, he put down the chalk smoothly, faced Hua Luogeng, and said respectfully.

Hua Luogeng smiled slightly: "Yes, the answer is correct, you go down first."

Zhao Anyuan turned and left, Hua Luogeng immediately came to the center of the podium, did not talk about the topic, quickly erased the topic with a brush, and immediately picked up the white chalk and wrote a new function problem.

The function y=x-2x, what is the value range of x∈[0].

"What's the solution to this problem? You need to draw an image." Hua Luogeng turned to look at the crowd after throwing away the chalk.

Looking at the question on the blackboard, this time, everyone's brows were slightly wrinkled. The difficulty of the question Hua Luogeng came up with was more difficult than the previous one, and he required a drawing.

A group of students thought quietly. This time, five seconds passed, and no one raised their right hand for the first time to indicate that they could disintegrate.

Hua Luogeng smiled without saying a word or urging, quietly waiting for the students below who were thinking hard. This question is a quadratic function value range problem, which belongs to a niche type and is not as important as basic elementary functions, but it is still important.

"Everyone can think about it, don't worry, if you forget this knowledge point, you can open the math book." After more than ten seconds, Hua Luogeng reminded with a smile when he saw that everyone still couldn't answer the question.

Hearing Professor Hua Luogeng's remarks, all the students were indifferent, unable to do their mental calculations, and immediately picked up pencils and scratch paper and began to calculate.

At this time, I saw a right hand raised below the classroom.

"The classmate who raised his hand, please come to the stage." Hua Luogeng saw the right hand and found that the other party was Yu Hua, whom he met in Ping'an a few days ago, nodded towards Yu Hua, and said in a straight voice.

As soon as the voice came out, the classroom was suddenly silent.

Yu Hua stood up and walked towards the podium. The students sitting in the first and second rows who were doing calculations saw that Yu Hua was actually on the stage, and their eyes were a little incredible.

It's been so long, Yu Hua actually has the idea of ​​disintegration!

The students sitting in the back row didn't feel anything, but many good students sitting in the front row felt ups and downs in their hearts, some were surprised, some were surprised, and some were incredulous.

Fang Yu, the No. 2 girl in the class, was like this. Her eyes widened, and she watched Yu Hua walk up to the podium in disbelief. Well, it’s okay if Zhao Anyuan solved the first question. After all, she is number one, but this second question Yu Hua, who was ranked 14th in the score, solved it faster than himself, what's the matter?

As the real little transparent in the class, Fang Yu, who is second in grade, will always be ignored by others. Classmates and teachers only remember Zhao Anyuan, who is number one, and Hangeul, who is the last one, but they don’t remember Fang Yu who is No.2 at all, as if her number People simply do not exist.

Under the watchful eyes of all the classmates, Yu Hua walked up to the podium, picked up the chalk and wrote directly.

solution:
∵y=x-2x=(x-1)-1, x∈[0],
∴ When X=1, the minimum value of the function y is -1, when x=3, the maximum value of the function is 3, so the value range of the function is [-1, 3]

After writing, Yu Hua turned around and bent over to take out the triangular board from under the lectern, and made a function image by inversely following the disintegration answer.

This question is not difficult in nature, but the difficulty is that the knowledge points are remote and require drawing.

Three times five and two, Yu Hua finished the function image.

The whole process takes no more than 2 minutes.

With the last stroke of the function image, a neat and standard function image and disintegration answer are presented to all students.

He really figured it out. ——The girl Fang Yu stared at the blackboard, subconsciously turned the pencil in her right hand, stared at the question and answer steps, and couldn't help recalling the knowledge points about quadratic functions.

The answer is correct.

"Sir, Yu Hua is done." After finishing, Yu Hua respectfully put down the triangular board and faced Hua Luogeng in front of him, speaking respectfully.

Professor Hua Luogeng looked at Yu Hua respectfully, nodded lightly, glanced at the answer steps and function images, and turned to look at everyone: "Very good, the answer is correct, do you understand?"

"Understood." The students in the front row replied in unison.

The students sitting in the back row were still looking at the blackboard, referring to the answers while doing calculations.

"Don't go down yet."

Hua Luogeng said to Yu Hua, glanced at the students in the back row, and waited for half a minute. After these students had a basic understanding, he smiled mysteriously at all the students, turned around and picked up the brush and chalk, wiped the blackboard again, and wrote A new topic.

The known function f(x)=xe-e+1, where t∈R, e=2.71828...is the base of the natural logarithm.

(1) When t=0, find the maximum value of the function f(x);
(2) Prove: When t<1-1/e, the equation f(x)=1 has no real roots;
(3) If the function f(x) is a decreasing function in (0, +∞), find the value range of the real number t.

Finished, pen down.

"Da!" The chalk landed on the surface of the desk crisply. All the students below the desk were like fools, staring at the blackboard blankly. They watched Hua Luogeng turn the blackboard into something they couldn't understand. .

Silly.

At this moment, everyone is stupid.

Standing next to the podium, Yu Hua's eyelids jumped and he couldn't help swallowing his saliva. Having experienced the tactics of high school math problems in later generations, he knew very well that the function problem in front of him was definitely the finale of the function type.

Looking at the function questions on the blackboard, Yu Hua only felt a sense of familiarity wrapped around his body, like a hundred years later. This is the feeling of being devastated by mathematics.

"Okay, let's solve this problem again, you have 5 minutes to think." Hua Luogeng smiled and pushed up his glasses, revealing the face of the future generations like Ge Jun boss, no, Ge Jun boss seems to be Hua Luogeng couldn't be ranked in front of him.

As soon as he finished speaking, Zhao Anyuan, who was suddenly lifted down, raised his right hand.

With this raised hand, all the students present were stunned, including Yu Hua.

Darling, has Zhao Anyuan been so good?

Just glanced at the topic, and it has been solved?
(End of this chapter)