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Chapter 4: Chapter 4: This Problem Is No Different From the Last One

At the front of the class, the chalk in Old Yang’s hand tapped against the blackboard. TAP, TAP.

”Problem 18, solid geometry. This was a freebie! How many times have I gone over this? Establish a three-dimensional Cartesian coordinate system! Find the normal vector! Why can’t you all remember? Huh? On a simple question like this, over a dozen of you still didn’t get any points?”

He was lecturing with great enthusiasm, but the eyes of at least half the students below were glazed over.

Only a few students in the front rows were still taking notes.

As for the students in the back rows...

Old Yang’s gaze fell on Li Dong’s seat.

Old Yang had always had a pretty good impression of Li Dong.

The kid wasn’t the sharpest, the type for whom it was hard to get things to ’click,’ no matter how you taught him. But his saving grace was his diligence.

But today, Li Dong was acting exceptionally strange.

Since the start of class, the kid had been doing God knows what, constantly scribbling all over his test paper. You might think he was correcting his mistakes, but Old Yang was only on problem 18, and Li Dong was already working on the final bonus question.

’Has he just completely given up?’

Old Yang sighed to himself.

In an environment like Seventh Middle School, once a student gives up on themself, there’s nothing a teacher can do to pull them back.

Old Yang shook his head and went back to explaining the test questions.

However, what Old Yang didn’t know was that the Li Dong he saw as having given up on himself...

...was, at that very moment, frantically berating himself thanks to his Concentration +0.1.

’You idiot...’

Li Dong stared at the steps he’d taken to solve the problem, wishing he could go back in time and slap himself twice.

’The need for monotonicity analysis was so obvious. Why did I take the logarithm of both sides? Was I just trying to make things harder for myself?’

It felt like a Challenger-tier player looking back at their Bronze-league gameplay—it was nothing but mistakes.

He still couldn’t see the answer at a glance like those academic aces, but he could clearly identify his mistakes and see the correct path forward.

While Old Yang was going over the test, Li Dong had already reviewed all the problems he’d gotten wrong at the beginning of the exam.

The thrill of solving the problems was so intense he couldn’t stop.

’This feeling... It’s not as good as that freak Newton’s Concentration +1, but for a failure like me, it’s more than enough!’

Li Dong gloated internally and turned his gaze to the final bonus question on the test.

[Given the function f(x) = eˣ − ax − 1 (where a is a constant). If f(x) ≥ 0 for all x ≥ 0, find the range of values for the real number a.]

Newton had already provided the answer to this question: a ≤ 1.

But he hadn’t shown the derivation.

In the past, Li Dong definitely wouldn’t have been able to derive the answer on his own.

But now, riding this wave of intense focus, he suddenly remembered the ”Deconstruction + Basic Looping” method from the study guide Joule had shared.

’Deconstruct the problem... Holds true for all x... which means the minimum value must be greater than or equal to 0...’

’Find the minimum value... take the derivative... f′(x) = eˣ − a...’

In less than five minutes, Li Dong was staring at the final derived result on his scratch paper, a ≤ 1. He was completely stunned.

’I... solved it? Just like that?’

He patted his cheeks in disbelief.

This test might have been made by the school and wasn’t especially difficult, but this was still a bonus question.

’I solved it just like that?’

’Was it just easier because I was working backward from the answer? Or is this +0.1 Concentration really this powerful?’

Li Dong felt terrifyingly capable.

’Deconstruction + Basic Looping...’

Li Dong muttered the phrase to himself and began rummaging through his school bag.

He’d always considered ”dihedral angle” problems in solid geometry his weak spot. Since Joule said to break problems down into their smallest components, he’d start by practicing how to find the ”normal vector.”

’Book Two... Where did Book Two go...’

He was so excited that his movements were a little too rough as he searched.

The noise was particularly jarring in the quiet classroom.

At the front of the room, Old Yang finally lost his patience.

He had just asked if anyone had solved the bonus question, but not a single student had volunteered to answer.

And then there was Li Dong, making all that noise and causing a scene.

”Li Dong!”

The furious shout made the entire class jump. Everyone’s head snapped toward Li Dong in the back row.

Li Dong, who had his head buried in his bag looking for a book, instinctively looked up with a bewildered expression.

”Huh? Here!”

”Li Dong, if you feel you’ve already completely mastered this problem and don’t need my lecture, then come up here and show everyone how it’s done.”

”If you haven’t solved it, then stop messing with your bag and pay attention!”

Old Yang pointed to the blackboard behind him.

He was just trying to get Li Dong to pay attention; he didn’t actually expect him to come to the board and solve the problem.

The surrounding students all ducked their heads, afraid Old Yang would turn his fury on them next.

Liu Liang, in the next seat, nudged Li Dong with his elbow and whispered.

”Dongzi, you’re toast. Old Yang’s making an example out of you.”

But thanks to his enhanced Concentration, Li Dong’s thought process had become incredibly... linear.

His brain was still contemplating a better way to apply Joule’s study method.

His interpretation of Old Yang’s tirade went something like this:

Information received: The teacher is calling me.

Directive analyzed: Go to the blackboard and solve the problem.

Operation executed: Okay, I’ll go solve it.

As for Old Yang’s true intentions and the difficulty of the question... all of that was filtered out by the +0.1 Concentration.

”Oh, okay.”

Li Dong agreed, then stood up and started walking to the front of the class.

He walked up to the blackboard as if in a daze.

Seeing that he had actually come up, Old Yang was momentarily stunned. He then turned to address the class in a grave tone.

”Class, I know this question is difficult. But it’s been a while now, and not one of you has even tried to think it through. You’re all just waiting for me to give you the answer...”

He was still speaking when he noticed the students looking as if they’d seen a ghost. He was just about to turn and see what was happening.

But then he saw Li Dong walk past him, coming down from the blackboard.

Old Yang was dumbfounded. ’What on earth is with Li Dong today?’ he thought. ’He seems completely out of it. Did he just come up here to immediately go back down?’

Just as he was about to give Li Dong a proper scolding, he heard a student in the front row exclaim.

”Oh, so that’s how you do it!”

”’That’s how you do what’?”

Startled, Old Yang instinctively followed the student’s gaze to the blackboard behind him.

[If a ≤ 1, then f’(x) = e^x - a ≥ 1 - a ≥ 0. The function is monotonically increasing, and the minimum value f(0) = 0, which satisfies the condition.]

[If a > 1, the local minimum is f(ln a) = a - a ln a - 1. Since this value is always less than 0 when a > 1, it does not satisfy the condition.]

[Final Conclusion: a ≤ 1]

Old Yang’s eyes widened as he stared at the solution on the blackboard.

This... How is this possible?

Had it even been a full minute between Li Dong walking up to the board and walking back down?

After his initial shock, Old Yang quickly regained his composure, but his brow furrowed even more deeply.

He checked the work from top to bottom.

It was all correct.

But Li Dong had skipped many steps. On an actual exam, he would’ve definitely lost points for that. But for someone who understood the problem, those steps were trivial; they would fill in the gaps mentally.

Li Dong’s derivation, therefore, looked more like a set of guiding notes than a full solution.

This kind of abbreviated solution might be plausible coming from an academic ace, but from Li Dong—a student who regularly failed math—it was utterly unbelievable.

Therefore, Old Yang felt no sense of pride. Instead, he was even more disappointed.

’No wonder the kid was on his phone all afternoon,’ he thought. ’He must have found the original question online and memorized the answer!’

Old Yang was bitterly disappointed, frustrated that his student wasn’t living up to his potential.

’So what if he failed this one monthly exam? Does he really need to resort to this to save face? He’s only fooling himself!’

”Fine. Well written,” Old Yang said, nodding expressionlessly at Li Dong, who had returned to his seat.

He didn’t intend to put Li Dong on the spot in front of the whole class.

But the other students knew Li Dong’s usual standard. There was no way he could have solved that problem so quickly.

Whispers began to spread among some of the students.

”He must have looked up the answer online.”

”Definitely. I saw him on his phone just a minute ago.”

Only one person, a girl in the front row, was sizing up Li Dong with a look of shocked suspicion.

Her name was Misha. She was the academic representative for their class and had scored a 109 on this very test.

She hadn’t been able to solve this problem, so she had secretly looked it up on her phone. The standard online solution used the parameter separation method, which was a very complicated process.

But the method Li Dong had written on the board...

...was completely different from the online answer!

’Did he come up with that himself?’ Misha chewed on her pen, a flicker of curiosity in her beautiful, fox-like eyes.

Just then, Old Yang, after a moment’s hesitation at the front of the room, called out to Li Dong again.

”Li Dong, come back up here for a second.”

Li Dong stood up, looking confused.

”Teacher Yang?”

”Since you have such a good grasp of this problem, it must mean you have a profound understanding of derivatives and inequalities.” Old Yang picked up an eraser and, with a couple of quick swipes, cleared a space on the board.

”As it happens, I have a variation of that problem right here. The difficulty is close to that of a bonus question on the actual college entrance exam.”

As he spoke, he wrote a new problem on the board:

[Given the function f(x) = e^x - a ln(ex), if f(x) ≥ 0 holds true for all x in the interval (0, +∞), find the maximum value of a.]

After he finished writing, Old Yang handed the chalk to Li Dong.

He wasn’t deliberately trying to make things difficult for Li Dong. It was just that this kind of vanity, once indulged, was bound to happen again.

He didn’t want this once-diligent student to start down the path of cheating just for a bit of ridiculous pride.

He even held on to a tiny, almost impossible shred of hope.

’But what if he can actually solve it?’

”Go on, Li Dong. Give it a try.”

Li Dong looked at the problem on the blackboard with a strange expression.

He turned to look at Old Yang, a hint of confusion on his face.

”Teacher Yang.”

”Hm? What is it? Find it too difficult?”

Old Yang sighed internally. ’So he can’t do it after all?’ Just as he was about to give Li Dong an easy way out...

”No,” Li Dong said, pointing to the blackboard.

”This problem is essentially the same as the last one. How about you give me a different one?”

He genuinely wanted a problem he didn’t know how to solve so he could master a new concept.

Old Yang was left speechless. Even his good temper was starting to fray.

”Then by all means, solve it and show me!”