"What is the solution to this question?" After writing, Hua Luogeng threw away the chalk and turned to look at the crowd.
Everyone in the classroom stared at the blackboard and carefully reviewed the questions. This function question, which was based on the modern definition of functions but had never been seen before, trapped many people.
It must be said that Hua Luogeng is worthy of being called a master of mathematics in this era, and the questions he randomly asked were quite difficult.
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 brief thought, he already had ideas for solving the problem in his mind.
Hua Luogeng pointed to Zhao Anyuan, who was sitting in the first row, and motioned to come to the stage: "This classmate, please answer."
Zhao Anyuan was not shy at all. As the strongest man in Neo-Confucianism Class 1, he walked onto the podium without hesitation and picked up the chalk to solve the problem under the gaze of Hua Luogeng and other students.
Solution: ∵y=bx+1>1, if A∩B has only one subset, then A∩B=?,∴a≤1, the value range is (-∞,1)
"Sir, Anyuan has solved it." Zhao Anyuan finished writing eloquently, 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 around and left. Hua Luogeng immediately came to the center of the podium. Without speaking on the topic, he quickly erased the topic with a brush, then picked up the white chalk and wrote a new function problem.
What is the value range of the function y=x2-2x,x∈[0,3].
"What is the answer to this question? You need to draw an image." Hua Luogeng threw away the chalk and turned to look at the crowd.
Looking at the questions on the blackboard, everyone frowned slightly. This question Hua Luogeng asked was more difficult than the previous one and required drawing.
The students thought quietly. Five seconds passed this time, and no one immediately raised their right hand to indicate that they could disintegrate.
Hua Luogeng smiled and said nothing, did not rush, and waited quietly for the students who were thinking hard below. This question was about the range of quadratic functions, which was a niche type. It was not as important as basic elementary functions, but it was still important.
"Everyone can think carefully and don't be in a hurry. If you forget this knowledge point, you can open the arithmetic book." After more than ten seconds, Hua Luogeng saw that everyone was still unable to answer the question and reminded him with a smile.
After hearing what Professor Hua Luogeng said, all the students were indifferent and could no longer do mental calculations. They immediately picked up pencils and scratch paper and began to calculate.
At this time, I saw a right hand raised from the bottom of the classroom.
"Students who raise their hands, please come on stage." Hua Luogeng saw this right hand and realized that the other person was Yu Hua whom he met in Ping'an a few days ago. He nodded towards Yu Hua and said seriously.
As soon as the words came out, there was silence in the classroom.
Yu Hua stood up and walked towards the podium. The students sitting in the first and second rows who were doing calculations had a look of disbelief in their eyes when they saw that it was Yu Hua who came to the stage.
How long had passed before Yu Hua actually had an idea of disintegration!
The students sitting in the back row felt nothing, 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 girl who ranked second in the class, was like this. Her eyes widened and she looked at Yu Hua walking up to the podium in disbelief. Well, it doesn't matter if Zhao Anyuan solved the first question. After all, she was first, but this second question
Yu Hua, who ranked 14th in the ranking, solved it faster than himself. What's going on?
As the real transparent person in the class, Fang Yu, who was ranked second in grades, was always ignored. Her classmates and husband only remembered Zhao Anyuan, who was ranked first, and Han Wen, who was ranked last, but did not remember Fang Yu, who was ranked second, at all.
People simply don't exist.
Under the gaze of all his classmates, Yu Hua walked up to the podium, picked up the chalk and started writing directly.
untie:
∵y=x2-2x=(x-1)2-1,x∈[0,3],
∴When
After finishing writing, Yu Hua turned around and bent down to take out the triangular plate from under the desk, and worked backwards from the decomposition answer to make a function image.
This question is not difficult in nature. What is difficult is that the knowledge points are remote and it requires drawing.
Three times five times and two times, Yu Hua has completed the function graph.
The whole process takes no more than 2 minutes.
As the last stroke of the function image was drawn, a neat and standard function image and its disintegration answer appeared in the eyes of all the students.
He really solved it. - The girl Fang Yu stared at the blackboard, subconsciously turning the pencil in her right hand, staring at the questions and answer steps, and couldn't help but recall the knowledge points about quadratic functions.
The answer is correct.
"Sir, Yu Hua is done." After finishing, Yu Hua respectfully put down the triangle, faced Hua Luogeng in front of him, and spoke respectfully.
Professor Hua Luogeng looked at the respectful Yu Hua, nodded slightly, glanced at the answer steps and function images, then turned to look at everyone: "Very good, the answer is correct, do you understand?"
"I understand." The students in the front row responded in unison.
The students sitting in the back row were still looking at the blackboard, referring to the answers and doing calculations.
"There's no need to go down yet."
Hua Luogeng said to Yu Hua, glanced at the students in the back row, waited for half a minute, and after these students basically understood, he smiled mysteriously at all the students, turned around, picked up the brush and chalk, wiped the blackboard again, and wrote
A new topic.
It is known that the 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 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 within (0, +∞), find the value range of the real number t.
After writing, the pen falls.
"Da!" The chalk fell crisply on the surface of the podium. All the students below the podium were like fools, staring blankly at the blackboard. They watched helplessly as Hua Luogeng changed the blackboard into something they couldn't understand with one stroke.
.
Stupid.
At this moment, everyone was dumbfounded.
Standing next to the podium, Yu Hua's eyelids jumped and he couldn't help but swallow his saliva. Having experienced the tactics of high school mathematics in later generations, he knew very well that the function question in front of him could definitely be regarded as the final question of the function type.
Looking at the function problems on the blackboard, Yu Hua felt a familiar feeling wrap around his body as if it were a hundred years later. This was the feeling of being tortured by mathematics.
"Okay, let's solve this problem again. You have 5 minutes to think about it." Hua Luogeng smiled and pushed up his glasses, revealing a face that would look like that of Mr. Ge Jun in the future. No, Mr. Ge Jun seemed to be here.
There is no seniority in front of Hua Luogeng.
As soon as he finished speaking, Zhao Anyuan suddenly raised his right hand.
With this raise of hands, all the students present were stunned, including Yu Hua.
Darling, is Zhao Anyuan already so awesome?
After taking a look at the question, you have already solved it?