After taking the advice, I became a top student.
Chapter 6 Isn't this obvious?
Chen Mo was unaware of his classmates' thoughts and simply continued explaining his own ideas.
"Then, based on the given conditions of the problem, we can see that the constructed function g(x) is monotonically decreasing from zero to positive infinity. Since f(x) is an even function, g(x) is also an even function. Therefore, we can obtain the graph of g(x)... And the a, b, and c required by the problem are g(1), g(2), g(-3)..."
With just a few simple words, Chen Mo had already given his answer.
This left the students in Class 18 completely stunned.
Then he looked at Hu Xin, hoping to get a negative answer from the teacher.
He must be talking nonsense!
Even Hu Xin glanced at Chen Mo more than once; this little guy seemed to be starting to show some interest.
He suddenly felt a little excited about the midterm exams in a little over a month.
"Hmm, it seems like there won't be a midterm exam. Let's give a pop quiz next class."
Hu Xin looked at Chen Mo with satisfaction, thinking to himself.
"Yes, Chen Mo's thinking is very good, and his answer is correct."
"Very good, sit down."
He spared no praise.
"Holy crap, he really will do it?"
"Obviously, easily obtainable, verifiable... Oh no, why do I feel like Chen Mo is starting to evolve in a non-human direction?"
"Yeah, how did he figure out that he needed to construct this kind of function?"
"I also want to ask, if f(x) is an even function, how come g(x) is also an even function?"
A commotion erupted in Class 18 as the students buzzed with discussion.
"right!"
Zhou Hao, standing behind, suddenly brightened up. As a top student, he thought this was obvious, and Shen Qingyi probably thought so too. But Chen Mo might not think so. "Chen Mo," he asked, "I'd like to ask, why is f(x) an even function, and why is g(x) also an even function?"
The classroom fell silent again.
After all, Shen Qingyi was sitting next to Chen Mo, so they couldn't help but have doubts.
"Isn't this obvious?"
Chen Mo was a little confused. Why was everyone so excited? This question wasn't difficult at all.
He was particularly puzzled that Zhou Hao, the top student in his eyes, would ask such a low-level question.
"How is it so obvious?"
Zhou Hao continued to press for answers, not because he was being irrelevant, but because Chen Mo's hesitation made him even more certain of his guess.
"An even function multiplied by an even function is still an even function."
Chen Mo, having been a poor student himself, thought about how impatient his classmates were with him and decided he didn't want to become the kind of person he disliked. So, he added, "Well, if you still don't understand, we can derive the expression for g(-x) as f(-x)/(-x)^2."
"(-x)^2 is x^2, and since f(x) is an even function, f(x) must be equal to f(-x). Therefore, the expressions for g(x) and g(-x) are the same, g(x) = g(-x). According to the definition, g(x) is an even function."
"Oh no, it seems he really can!"
The students looked at Chen Mo blankly.
Now, no one doubted that Chen Mo had copied Shen Qingyi's answer.
Zhou Hao's face darkened when he saw the look of concern in Chen Mo's eyes for intellectually disabled children; he felt insulted.
How could I not know such a simple question? I just wanted to test you!
Ring ring ring...
The bell rang, signaling the end of get out of class.
"Okay, everyone learned very well in this lesson. Chen Mo's problem-solving approach is also correct. That's all for this problem."
Hu Xin nodded in satisfaction. He hadn't expected Chen Mo to actually be able to do it, and that he had used all the knowledge points he had taught in this lesson. It felt great that his hard work hadn't been wasted.
He then turned to the next page of the textbook. "Everyone, please do exercises 1.1, 1.3 after class... The class representative should collect the homework and bring it to my office tomorrow morning."
After assigning the homework, Hu Xin took the textbooks and left the classroom.
Zhou Hao breathed a sigh of relief, feeling as if he had been granted a pardon, and quickly left the classroom, pretending to go to the toilet.
Chen Mo kept his promise and carried his desk back to his original spot.
"Holy crap! Were you secretly studying behind our backs?"
Huang Qinghua stared wide-eyed at Chen Mo, looking him up and down. He had said that he hadn't seen Chen Mo since early morning, and that the kid must have been secretly working hard behind their backs.
Li Ze looked at Chen Mo with some suspicion. He still couldn't understand why Chen Mo had changed so much in just one day.
Chen Mo took out the homework assignments given by Hu Xin, randomly selected one, and walked towards Shen Qingyi with his textbook.
Shen Qingyi was a little unaccustomed to the sudden absence of someone beside her.
Although it was only for two class periods, she felt it was nice to have Chen Mo next to her.
Chen Mo's grades may not be very good, but his attitude towards learning is really good. Under his influence, Shen Qingyi felt that she was more focused and attentive in class.
However, her disappointment did not last long.
Because Chen Mo had returned to her side, holding a draft notebook and a pen.
"Qingyi, may I ask you a question?"
"I found the homework assignment the teacher just gave me a bit difficult. Could you explain it to me?"
Chen Mo placed the math textbook and draft paper on Shen Qingyi's desk and asked.
Given a function f(x) such that for any x, y, y∈R, f(x+y)=f(x)+f(y), and f(x)>0 when x>0.
(1) Find the value of f(0).
(2) Prove that f(x) is an odd function.
(3) Prove that f(x) is monotonically increasing on R.
Shen Qingyi glanced at the question, then looked up at Chen Mo. Even with her good manners, she almost couldn't help but roll her eyes.
It wouldn't be accurate to say this question was easy, but all three parts could be solved directly using the definitions. If it were the old Chen Mo, she believed he probably wouldn't have known how to do it.
But he just solved a much more difficult problem, and his solution was clear, which shows that he has a good grasp of the knowledge points taught by the teacher in this lesson.
It's like a primary school student who already knows compound operations asking her what one plus one equals.
Considering that Chen Mo had suddenly moved to sit next to her, she couldn't help but suspect that he might have ulterior motives.
"Chen Mo, it's good to be willing to ask questions, but you must think things through before asking them in order to gain something."
Although Shen Qingyi said this, she still started scribbling on the draft paper. "Finding f(0) is very simple. Just let x and y both equal to 0, and substitute them in. Isn't that f(0) = f(0) + f(0)? Then f(0) equals 0, right? The first question is solved..."
Think before you ask questions. Task difficulty F, completion reward: +1 nutrient.
Chen Mo was a little distracted. Seeing the new suggestion that had formed in his mind, he felt that asking the question was already worthwhile.
Don't be fooled by the small reward for this suggestion; it's also quite easy to complete. As long as you ask enough questions, you can accumulate a considerable amount of knowledge over time.
Shen Qingyi is indeed a good classmate, contributing greatly to her academic success!
"That makes perfect sense! Qingyi is amazing!"
Chen Mo praised her sincerely.
For some reason, Shen Qingyi felt a bit itchy when she heard these words.
The question was not difficult to begin with, and Shen Qingyi quickly finished explaining the three sub-questions.
At this moment, a notification popped up in front of Chen Mo's eyes.
[Daily task completed (2/3): Ask the class beauty a question every day, +10 points]
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