[Take two points on a continuous and smooth curve. On the curve segment between these two points, you can find at least a point so that the tangent of the point is parallel to the straight line formed by the two points.]

Martin picked up the paper and showed the contents on it to Doriani.

Doriani was still surprised by the sudden appearance of paper and pen.

But looking at the content on the paper, I immediately began to frown and think.

Although this passage does not mention functions, she naturally immediately connected with functions due to the recent learning period.

"No need to think about it for now. This is a theorem, which I call the Cauchy median theorem, and I will prove it next."

Martin reminded on the side, and took out another piece of paper and started writing quickly.

Doriani looked at the ink traces unfolded in Martin's pen with curiosity.

Martin was a little nervous, but he still quickly wrote these contents that he had thought about repeatedly many times into words and symbols.

The Cauchy median theorem belongs to the general form of the Lagrangian median theorem.

It is also the most important of the three median theorems.

Two minutes later, Martin picked up the paper with a detailed derivation and proved process and handed it to Doriani.

A full page, densely filled with handwriting.

The proof process is not complicated.

In fact, as long as you understand the basic concepts related to functions and limits, the median theorem is a very simple theorem.

Otherwise, it wouldn't have appeared in advanced mathematics courses.

However, in order to allow Doriani to clearly understand the proof process, Martin also wrote down the part that could have been omitted carefully.

After all, even though Doriani has extremely high talent in mathematics, he still has a short time to get involved in these things and needs an adaptation process.

Doriani understood while watching and soon finished the proof process.

Just as her eyes were removed from the paper, Martin heard the system's prompt sound.

[The advanced conditions have been completed, and advancement will begin soon...]

Buzz!

After a sound.

Time seemed to be still for Martin.

The island seemed to have stopped.

Colorful clouds, the sky changing between indigo and orange, the winding river floating in the distance...

All of this looks like the background screen in the game.

The golden crown appeared on top of my head at some point.

Under the influence of some special force, rays of colorful light gradually emerged from various things in the spiritual world and then gathered towards the island.

The ethereal feeling made Martin feel unprecedentedly calm.

He looked at the clouds, rivers, earth in the spiritual world, and these colorful things seemed to have a new look in his eyes.

The colorful light was absorbed by the crown and then converted into pure energy and instilled into the body.

Martin felt that his spirit body was becoming more and more solid, and he had a unique sense of reality.

The fluctuations belonging to the knowledge field were constantly emanating from him, and they began to affect the surrounding space.

He could clearly feel that a new ability was being generated in his body.

That wonderful feeling is really indescribable.

Just then!

But Martin glanced at Doriyani.

He noticed that Doriani, who was originally the background board, seemed to have taken a momentary action.

wrong!

To be precise, it's not an action.

But the power fluctuations in the realm of fate!

Although it was only a short moment, it seemed to have had some direct impact on myself!

However, Martin doesn't know what the specific impact is...

This state of static space and time lasts for unknown periods.

When Doriani continued to move, Martin seemed to be in a different world.

"Why should we call Cauchy's median theorem? Who is Cauchy?" asked Dorini.

Martin blinked, looked at the paper in Doriani's hand, and came back to his senses.

He casually said: "I heard from a man named Cauchy by chance, don't care about these details."

Dorian nodded in confusion, then asked curiously: "So is this theorem of any specific function?"

Although she is very keen in mathematics, she has just been exposed to calculus and many theorems used in tools cannot understand what their functions are.

"It can be used to find the limits and deduce some more complex functions..." Martin explained briefly.

"Why do you want me to come here to see this?" Doriani looked at Martin, the golden crown on his head was a little dazzling.

Martin shook his head slightly: "It's nothing, it's just a small experiment."

Of course he would not say it was because of his advanced conditions.

Even if Doriani is absolutely trustworthy, he will not undermine this principle.

Moreover, Martin only thought two days ago that knowledge is a sequence of birth in the spiritual world.

So he thought that perhaps the conditions to complete in the spiritual world would be smoother.

Now it seems that his guess is completely correct.

This is not, it just proves a theorem and allows Doriani to understand it and complete the advancement.

Everything seemed so relaxed and natural that it even gave him a less real feeling.

As for the previous Lagrangian median theorem, he has described it once.

Strictly speaking, it has appeared in this world.

Therefore, Martin changed to the more representative Cauchy's median theorem.

"Do you feel more relaxed in understanding here?" Martin asked, pointing to the piece of paper.

He needs to confirm something.

If it is not a coincidence, then for Martin, this place can produce new effects.

Doriani frowned and recalled: "It seems that the idea has become clearer."

Martin nodded.

It seems that he is not bad as expected. The spiritual world's bonus to the spirit is not only effective for him, but also for other people who enter here.

Doriani is the best proof.

"You go out first, I have something to deal with." The matter has been dealt with, Martin said to Doriani.

And keeping Doriani here is quite expensive.

Doriani looked at the golden crown on Martin's head. He wanted to touch it, but finally he didn't have the nerve to say it out.

It is easy to return from the spiritual world to reality. Just silently recall and perceive your body in your heart.

Doriani's translucent figure disappeared on the island.

Martin immediately exhaled the system interface and began to check his changes after he advanced.

【Name: Martin Olic】

【Species: Humans】

【Gender: Male】

【Age: 23 years old】

【Sequence 7: Wise, Experience Value: 0/1000】

...

Like "scholar", the two words "wise" are also written in Di Mongolian texts.

A person with rich knowledge.

Martin's eyes moved downward toward the more important extraordinary ability.

【Extraordinary ability: ban!】

[After the target is activated, block one of its capabilities. If it has been activated, it will invalidate it.]
To be continued...