Is not being able to do as you please also called rebirth?

Chapter 8 Teacher, can I try?
The expert is indeed an expert; his ability to cultivate inner strength is truly impressive.

Although he had already seen that there was an English book on Jiang Xun's desk, and he knew that Jiang Xun hadn't been listening to his lecture at all,
But he still smiled and repeated his question.

"Please answer the question about using derivatives to find the monotonicity of a function."

This question is fairly basic; theoretically, any student who listens attentively in class should be able to answer it.

But don't forget that they have only just begun their first round of review, and this part of the knowledge has not yet been reviewed. Many students have already forgotten most of it.

Therefore, when this question was asked, only a very small number of students in the class raised their hands to answer.

Moreover, these were all people like Yang Kaiyi and Zhang Tao who had already answered questions before.

Of course, it's also possible that some people know the answer but are too afraid to raise their hands.

So the expert skipped them and went straight to Jiang Xun, who wasn't attending the class.

"Jiang Shen is in big trouble now. He's made our school lose face in front of the experts from the city. I wonder how Old Zhu will deal with him."

"That kid made a big splash last night, he deserves to be down on his luck today."

"Chen Shixuan doesn't seem worried about him at all; she's even secretly smiling."

"I feel like Brother Bo would strangle him right now, how could he be daydreaming in a class like this?"

The students observed the reactions of everyone in the class and the teachers while silently mourning Jiang Xun.

Just then, Jiang Xun's clear and steady voice rang out in the spacious lecture hall:
"To determine monotonicity using derivatives, the general steps are as follows—"

"First determine the domain, then find the derivative."

"By setting the derivative function to be greater than zero, we obtain the range of values ​​for X. Taking the intersection of this range with the domain, we obtain the monotonically increasing interval."

"By setting the derivative to less than zero, we obtain the range of values ​​for X. Taking the intersection of this range with the domain, we obtain the monotonically decreasing interval."

"If multiple intervals have the same monotonicity, connect them with a comma or 'and'."

"That's right, teacher."

His voice faded, and the classroom fell silent again.

At this moment, everyone's eyes were focused on him, and their eyes were filled with more or less surprise.

It wasn't because his answer was particularly good; after all, the question itself wasn't difficult.

Rather, it was because his voice was steady and clear, his posture was very upright, and he answered the questions very completely.

This was a stark contrast to the fact that he hadn't even heard the question clearly at first, which surprised everyone.

The expert teacher seemed a little surprised. He smiled and praised the students, then gestured for them to applaud.

The classroom erupted in enthusiastic applause. Apart from a very few students who were a little annoyed, most people actually thought Jiang Xun was more impressive.

It's not easy to remain so calm in this situation and answer questions so well.

Didn't you see other students either stammering or having their brains short-circuit when answering questions?

Jiang Xun's performance has certainly brought honor to Class Three.

Shi Tingbo, sitting at the back of the classroom, breathed a sigh of relief, but was also secretly surprised.

He hadn't expected that Jiang Xun's rapid review and cramming during this period would actually be effective, which rekindled his hope for Jiang Xun.

It seems we need to pay more attention to this kid in the future and try to get his math score above 100 before the college entrance exam.

Yang Kaiyi and Chen Shixuan were also looking at Jiang Xun, but their gazes were completely different.

Yang Kaiyi felt a touch of admiration. How could this guy be so calm? Every time she stood up, her cheeks would burn with nervousness.

Chen Shixuan, on the other hand, suddenly realized that Jiang Xun was actually quite handsome when he answered questions seriously.

However, as the class continued, the teacher did not call on Jiang Xun to answer any more questions, because he still wasn't paying attention.

The knowledge points reviewed later were all about using derivatives to find the monotonicity of functions, including functions with parameters.

As the difficulty increased, the classroom became almost entirely dominated by the teacher and a few students, with most questions being answered by only a handful of people.

In the final stage, the teacher presented a problem for everyone to practice in class, and asked someone to come up and demonstrate the solution steps in class.

The problem seems simple: the function f(x) equals 1 minus e raised to the power of -x. The first question asks for proof that when x is greater than -1, f(x) is greater than or equal to x/(x+1).

For the second question, suppose that when x is greater than or equal to 0, f(x) is less than or equal to x/ax+1. Find the range of values ​​for a.

After everyone read the question, they all buried their heads and looked completely bewildered.

The first question leaves most people clueless about where to begin, and the second question leaves them even more confused.

Jiang Xun had already put down his English book; he felt nauseous and wanted to vomit.

Seeing the problem on the blackboard, I felt it was somewhat interesting, so I lowered my head and started working on it, just in time to test the results of my recent book reading.

The first question is simple.

Substitute f(x) into the inequality, rearrange terms, and construct a function;
Find the derivative and the minimum value, then substitute the point of maximum or minimum value into the equation to prove that the original inequality holds!

The second question was a bit more difficult. Jiang Xun frowned and thought for four or five minutes before starting to write.

To determine the possible values ​​of 'a', we need to construct a function, find its derivative, and identify the monotonic intervals.

Although the method is similar to the first question, the difficulty increases dramatically due to the uncertainty of parameter 'a', which requires discussing multiple scenarios.

It took Jiang Xun nearly ten minutes to write out the complete solution.

At this point, the teacher had already called up two people to answer the first question: Zhang Tao and Chen Liang, the class monitor.

Chen Liang failed to complete the task and walked off the stage with a flushed face.

Although Zhang Tao's process had some minor flaws, he ultimately wrote out the correct proof approach.

However, the teacher asked him to continue with the second question. He stood on the podium, wrote the beginning, but couldn't continue. He was so nervous that sweat was pouring down his forehead.

"Is there anyone willing to come up and help this student?" At this moment, the teacher looked down at the crowd, surveying the front row.

Everyone kept their heads down, afraid of being called on. Even Yang Kaiyi pretended to be doing his homework and didn't dare to look up.

If even Zhang Tao, a math whiz, can't do it, then she certainly can't either.

However, the teacher had her eye on her, because she was pretty and proactive, and the teacher was very impressed with her.

"Why don't you give it a try, young lady?" The teacher walked up to Yang Kaiyi and looked at her with a smile.

Yang Kaiyi raised her delicate oval face, her slightly chubby cheeks flushed, clearly indicating that she was very nervous.

She bit her lip, preparing to stand up and say she couldn't do it. Although it was embarrassing, it would be even more embarrassing to go up there and not be able to do it.

"Teacher, let me try." Just then, a familiar voice came from the back corner.

Everyone turned to look and were surprised to see Jiang Xun stand up on his own initiative.

Yang Kaiyi looked at him with surprise, a ripple of emotion stirring within her.

Given the difficulty of this question, Jiang Xun probably wouldn't be able to answer it.

He stood up at this moment, most likely just to cover for himself. Yang Kaiyi was touched, but also worried for him.

"Oh, so you're playing the hero saving the damsel in distress." Chen Shixuan snorted angrily as she watched Jiang Xun walk steadily toward the podium.

Under the watchful eyes of the crowd, Jiang Xun walked up to the podium, picked up a piece of chalk, and first wrote a large character '解' on the blackboard.

Then he lowered his head and pondered for ten seconds, recalling the complete solution process.

During those ten quiet seconds, whispers broke out, and some people even started to chuckle softly.

"It's alright, you two students can go down now." The expert teacher smiled kindly and said:
"This question was actually the final question in this year's college entrance examination for science students, and not many students in the whole province could solve it."

Zhang Tao breathed a sigh of relief, his face flushed, and fled the podium as if running away.

But Jiang Xun not only didn't leave, he raised his right hand instead.

Hey!
The chalk fell onto the blackboard, making a crisp sound.

The characters, as sharp and elegant as silver hooks and iron strokes, poured out from under the chalk, as if sealing away all the sounds in the classroom in an instant.

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(End of this chapter)