x∈[-π/3,2π/3],

(1) Find the value range of function y=cosx;

(2) Find the value range of function y=-3sin2x-4cosx+4.

This is a big question, with a score of fifteen points!

In general, high school mathematics, 100 points are basic questions, which means that as long as you study it carefully and practice it frequently, it is not difficult to finish this percentage!

As for the remaining fifty, it is more difficult, because these fifty or thirty are generally the final big question!

It’s okay for the first and second grades of high school, but the big questions for the third grade are basically not prepared for ordinary students.

To put it bluntly, most of the people who can do the last major math question in the exam are to focus on the main topic, and even the target is Peking University and Tsinghua University.

Of course, this test paper is only a first-year high school student, and the mathematical knowledge you are involved in is relatively basic.

Lao Mo Cao walked around a long circle and looked at the papers of several classmates. At the same time, he also saw many mistakes. He felt a little heartbroken for a while. If it weren't for the exam room, he might have cursed.

Is pig brain? Did you carry your brain during class?

Especially for his anxious students, the most important thing is that there are two other people who he thinks are good at math.

When I walked to Xu Qian, I saw the neat answers full of papers!

Well, Xu Qian is still smart!

If he didn't write some fill-in-the-blank questions, he would not be able to see the correct answer at a glance, but he stood behind Xu Qian and silently calculated that Xu Qian's answer was correct.

When he came here, Xu Qian had already started to do the following big questions.

"So fast?"

"Don't you use draft paper?"

Xu Qian had already started and wrote it directly on the paper.

The draft paper posted next to it is still blank.

"Solution: (1) ∵y=cosx is an incremental function on [-π/3,0] and a subtraction function on [0,2π/3].

∴When x=0, y takes the maximum value of 1; when x=2π/3, y takes the minimum value -?.

∴y=cosx's range is [-?,1].

(2) The original function is: y=3cos2x-4cosx+1,

That is, y=3(cosx-?)2-?, from (1), cosx∈[-?,1], so the value range of y is [-?,15/4]."

"Is this guy different from that of ordinary people?"

Lao Mo Cao was shocked and secretly praised Xu Qian's power, but he was more happy.

It's too late this semester. If Xu Qian can maintain it next semester, he should have something to do for Xu Qian.

For example, it is recommended to participate in some competitions.

If such talents are not outstanding, wouldn’t it be a bit too wasteful?

Guo Lanlan was still thinking about copying an answer, but she never expected that the invigilator would stay by her side, which made her have to lower her head.

only……

Her mathematics itself is not good. Even for the previous multiple-choice questions, many of them stare at me. They can only use the rules of choice, three long and one short and choose the shortest!

The previous multiple-choice questions can still be puzzled, but the subsequent answers are completely silly. To put it bluntly, I don’t know what to write if I want to fill them up.

Finally, the teacher left and she looked over.

The guy sitting next to him was actually full of papers.

Could this Xu Qian be a top student?

But why haven't you heard of it before?

"It's over!"

Xu Qian yawned and didn't sleep well last night. After all, he ran out to surf the Internet in the middle of the night, but he didn't even stay all night. Instead, he came back at around 1:00 in the evening.

If there is no such system, even if he does not make money in this life, he will definitely protect his body and strive to have a strong body!

but……

In physical education classes, he can improve his physical fitness without exercise or running. He can do this body with great strength.

After finishing the math test, it took only an hour.

And it is obvious that Xu Qian’s math test is much faster than Chinese history and other papers.

After all, the math paper needs to be written less than the Chinese history papers, especially in Chinese, which often has eight hundred essays and is handwritten. If you type on the keyboard, it will take ten minutes!

Just as he looked at Cao Laomo, Xu Qian had no choice but to start writing random drawings on the draft paper.

[You don’t do questions in the mathematics exam room and do it, and you can integrate the knowledge points of mathematics in the second year of high school!]

[You sleep on your tummy without doing the exam in the math exam room, logical thinking +1]

...

"Hey!"

Lao Mo Cao came over at some point and knocked on Xu Qian’s table: “Do the questions well!”

"What else do you do after you finish writing!"

Xu Qian pointed to his own paper.

Laomo Cao frowned: "Then check it!"

"What else can I check for it all!"

Laomo Cao:...

Looking at Xu Qian's look of his own apology, his veins were almost bursting.

He has been coaching for twenty years, but he hasn't seen such an arrogant guy.

"Ouch, Teacher Cao, I have a stomachache!"

Xu Qian's face changed and he held his stomach: "Teacher, I'm going to hand in the paper. I can't do it anymore. I'm almost pulling it out. I'm all at the door!"

As he said that, he even farted!

Old Demon Cao also changed his face and he stepped back decisively: "Get out!"

"Okay!"

Xu Qian quickly ran away with his pen.

wait?

I really have to wait for the ringtone in the exam room!

How is this possible!

"Oh, it's not time yet!"

Another invigilator quickly called someone.

"Forget it, let him go!"

"You student?"

Lao Mo Cao nodded, picked up Xu Qian's paper and started to do the test. He took the paper and pen and started to do the test.

Half an hour later, Cao Laomo looked shocked!

"It's really right!"

"How is this possible?"

"Although this math test is not too difficult, it is still very difficult to get a full mark!"

There are also full marks in mathematics, but not every grade exam has full marks.

And even students with full math scores will not come from his class.

After all, most of the students who are good at studying are in Class 1 and 2.

"Hey, I'm going to turn over this wave!"

Perhaps it is precisely because he is an old teacher that Lao Mo Cao attaches great importance to this aspect.

The whole world is full of students, the hard-working gardener!

He started teaching in the early 1990s and was quite responsible to his students. Naturally, he was not convinced that there were no students under his school!

"It seems that Xu Qian is indeed a charming talent. Although he can do whatever he wants in class, maybe... he has his own way of learning?"

As long as the result is good, no need to explain it yourself, others will make excuses for you!

Obviously, Lao Mo Cao could not escape this law.

He is no longer angry now, thinking about caring about Xu Qian in the future.
To be continued...