Super academic master: start with low adjustment scores!

The invigilator was speechless.

He was shocked.

What is Xiu'er?

This is Xiu'er.

He has been teaching for nearly 20 years.

He has seen all kinds of math geniuses.

But compared with Jiangnan, those so-called geniuses are all scum, not at the same level at all.

This point...

It can be seen from the fact that Jiangnan finished the last question of the paper less than ten minutes after the exam started.

And...

According to Cao Tianyuan.

Jiangnan's accuracy in solving problems is still 100%.

Even...

The draft paper specially distributed for the math exam is clean, without a single word written on it.

You should know that some students next to him have not finished the multiple-choice questions, but have already used up a piece of draft paper.

Hiss...

What kind of logical thinking and spatial thinking does a person need to have to reach Jiangnan's level?

At the same time.

Jiangnan as the person involved.

But he ignored the shock of the two invigilators behind him, and just wrote quickly.

For him.

These questions were too unchallenging.

He just wanted to finish them quickly, and sleep was the best choice.

However...

When he got to the last question of the paper.

His eyes froze slightly.

"Huh!"

"Finally, I came across an interesting question. It seems that this paper is not useless."

Before this, Jiangnan read the questions in one second, and then he could get the answer in his mind instantly.

However...

This last question.

He looked at it for several seconds.

It can be seen...

This question is much more difficult than the previous ones.

The original question is as follows...

"Given the function f(x) = 1/√(1+x) + 1/√(1+a) + √(ax/(ax+8)), x belongs to (0, +∞).

(1) When a=8, find the monotonic interval of f(x).

(2) For any positive number a, prove that: f(x) is greater than 1, but less than 2."

Similar to the first question of the answer sheet.

This last question is also a function problem.

But...

The difference is.

This involves monotonicity and inequalities.

It feels a little more difficult than the previous questions.

However...

For Jiangnan.

It is only slightly interesting.

The word "difficult".

This could not possibly appear in his mind.

Solution...

When a=8.

f(x) = (1+√x)/√(1+x) + 1/3.

The derivative is f`(x)=(1-√x)/2√(x(1+x)^3.

So when x belongs to (0, 1).

f`(x) is greater than or equal to 0.

When x belongs to [1, +∞).

f`(x) is less than or equal to 0.

So f(x) is monotonically increasing on (0, 1) and monotonically decreasing on [1, +∞).

…

What is a pen moving like a dragon?

This is a pen moving like a dragon.

After Jiangnan wrote the word "solution", he did not pause and directly solved the first question.

Tsk tsk!

One word, absolutely.

The invigilator behind him couldn't keep up, because he didn't teach math, and Jiangnan's speed of solving the questions was too fast, so he couldn't understand it at all.

But...

It was precisely because he couldn't understand it.

He was much calmer.

On the contrary.

When Cao Tianyuan saw that Jiangnan solved the first question of the last question in an instant, his pupils shrank again, his expression was moved, and his heart was even more in turmoil.

Damn it!

Awesome, so strong!

Jiangnan was really going to be amazing.

The invigilator next to him knew that the math final question was difficult, But I don't know how difficult this question is.

However...

Cao Tianyuan knows.

After all...

He is a senior math teacher.

Although this question does not seem complicated at first glance, it is just at first glance.

In fact...

It is really very difficult.

Even if he were to do this question, he would not be able to solve it without spending 80% to 90% of his effort.

It is not an exaggeration to say that this is the most difficult final question of the monthly exam he has ever encountered. It is several times more difficult than the final question of the college entrance examination, and can even compete with the final question of the Olympic Games.

But...

Jiangnan Yet he did it without any effort?

It was incredible.

He was not a human being!

He was really not a human being.

He no longer dared to regard Jiangnan as a student.

How could he still be a student?

He was obviously a senior professor of mathematics!

He was far inferior to him.

But...

It was not over yet.

While Cao Tianyuan was sighing, Jiangnan had already started to do the second question, and his speed was still very fast.

(1) First prove that f(x) is greater than 1.

Because 1/√(1+x)＞1/(1+x).…

So …

f(x)=(1+(a+b+x)+(ab+ax+bx)+abx)/(1+x)(1+a)(1+b).

(2) Prove that f(x) is less than 2 …

…

That is, ab+8 is greater than (1+a)(1+b).

That is, a+b is less than 7.

…

In summary, for any positive numbers a and x, f(x) is greater than 1 but less than 2.

Jiangnan answered.

He did it in one go, like flowing water, and easily solved the second question.

In other words …

Jiangnan has finished the exam?

See this.

A certain invigilator at the back subconsciously looked at the clock on the blackboard and found that it was only … nine minutes before the exam started?

Damn!

Only nine minutes?

Less than ten minutes.

Jiangnan finished the entire paper?

Such horror!

This guy is not a human being!

If he hadn’t seen it with his own eyes, he wouldn’t have believed it even if he had beaten him to death and burned him to ashes.