“…”
“First, look at the problem statement: Given the function f(x) = x² – 2ax + 2, for x ∈ {-1, +∞}, f(x) > a always holds.”
“Then the final scoring item for this problem: ‘What is the range of values for a?'”
The tip of the pen pressed against the paper.
The pencil, normally used for drawing auxiliary lines, sketched short horizontal lines on the exam paper with the girl’s movements.
“The scoring points for this type of problem are… here, correct differentiation gives 2 points, monotonic intervals and extreme points usually give 3 to 4 points.”
“Case discussion: 3 points, final conclusion: 3 points.”
“Of course, if your process is completely wrong, even if the result is correct, they won’t give you points for the result.”
Yin Xiaomeng looked at the handwriting on the paper with a headache.
Calling it ‘dog-scrawl’ would be a compliment.
Just identifying the tangled mess at the beginning made her temples throb.
The girl, who initially wanted to mock the other for not being able to get points on such a simple problem, after witnessing this ancient god’s record, felt some sympathy for the grading teacher.
“…”
“Forget it, I’ll take my scratch paper and write it from the beginning for you…”
Hard work may not always pay off, but facing this insurmountable peak, decisively choosing to give up will definitely make you feel relieved.
She placed the pencil flat on the desk.
Enduring the scorching gaze from the girl beside her—’Is my handwriting really that ugly?’
—She bent down with difficulty and brought the bag hanging on the side of the desk onto her lap.
The sound of the zipper being pulled open was extremely faint under the chatter of the arriving classmates.
The girl sitting next to Yin Xiaomeng watched with a smile as she searched through the bag for which practice book the scratch paper was clipped into.
The fingers curled inside her sleeve trembled imperceptibly.
As if she was holding something back.
Situ Ling licked her lips and tried to force her gaze back to the exam paper spread out on the desk.
But her peripheral vision still uncontrollably glanced at the girl still searching.
“Yeah, found it!”
“Where were we just now?”
“…”
“Oh right, let me list the writing process for this type of problem from the beginning.”
Yin Xiaomeng didn’t notice anything unusual.
After more than a year of interaction, her trust in her best friend (close female friend) had reached an extremely high level.
After all, in that first year of knowing each other, she had prepared countless plans for various situations.
The number of times she had exposed weaknesses in front of the other might have been more than the number of times Situ Ling ate in first grade.
The testing was enough.
Since she could confirm that the other was sincere towards her, she naturally had to be sincere in return, right?
How does that saying go?
[I may be bad, but I still have morals.]
“f(x) = x² – 2ax ≥ 0, that is: x² – 2ax + (2 – a) ≥ 0, ∀x ≥ -1.”
“The parabola opens upward, with axis of symmetry x = a.”
After sketching a Cartesian coordinate system on the scratch paper with a few strokes, the girl looked up at Situ Ling, who was lowering her head with an expression of ‘I am seriously listening!’ but was fiddling with her fingernails inside her sleeve.
She squinted and tapped the other’s forehead lightly with the pencil.
“Don’t zone out, listen to the problem!”
“If you want me to help you with the problem, then honestly put your mind here. If you daydream again, then don’t listen!”
While maintaining her outward persona of being gentle and considerate, she also had to struggle to put on a sufficiently authoritative appearance to scold the distracted girl.
Yin Xiaomeng, who was not gentle at all at heart, felt like her left brain was about to attack her right brain.
“Mm-hmm, listening, listening.”
“I promise to complete the task!”
The girl who was caught thinking about other things chuckled.
One hand covered her forehead that had just been tapped, while the other hand skillfully grabbed the girl’s clothes and shook them like a spoiled child.
“Then I’ll continue. Later, you’ll repeat what I told you back to me.”
“…”
She withdrew her gaze and ultimately did not slap away the little hand gripping her clothes.
To be honest, after being a scumbag who juggles multiple relationships for so long, being suddenly approached by someone close for no reason…
Actually felt a little happy.
The corners of her mouth lifted slightly, but Yin Xiaomeng still kept a straight face as she placed the pencil tip back on the scratch paper and started writing again.
“Now this is divided into two cases: one where the axis of symmetry is to the left of the domain, that is a ≤ -1, and the other where a > -1.”
“In the first case, f(x) is monotonically increasing on {-1, +∞}, which means we only need the minimum f(x) ≥ 0…”
“…”
The nib scraped against the paper, making a pleasant rustling sound.
The side profile of the girl writing seriously was bathed in a thin halo of sunlight from the window.
Her already beautiful face at that moment was like a tranquil fairy descending to the mortal world.
“…So, we can draw the first conclusion: -3 ≤ a ≤ -1.”
The elegant handwriting fell neatly on the pure white scratch paper without any alignment aid.
The tails of each letter, with a hint of artistic flair, were not jarring even as a whole.
“Then the second case: the axis of symmetry lies within the interval, that is a > -1.”
“The minimum…”
“…”
“Finally, the second conclusion: -1 < a ≤ 1.”
“Then merge the two results to get the final answer interval: -3 ≤ a ≤ 1.”
“Then answer: the range of real number a is {-3, 1}.”
Situ Ling shifted her attention back to the words written by the girl’s pen.
Not caring what she had said while she was distracted, she just nodded vigorously like a garlic stamp.
“Mm-hmm, got it!”
“…”
Yin Xiaomeng looked at the other’s clear-eyed expression, like a university student, and for a moment didn’t know whether to sigh or tap her head again.
After thinking, she reached out and rubbed the other’s head.
It felt a bit like petting the golden retriever her parents kept…
“Forget it, let the kid be a bit slow.”
“At least she’s a kid who hangs out with me every day and still stays innocent.”
“Explaining problems to her more counts as paying emotional damages.”
“…”
“Sigh.”
“Then take the scratch paper and look it over a few more times. I’ll find some similar problems for you. Do a few more of the same type, and later when you encounter this kind of problem, you won’t feel confused.”
The girl reluctantly moved her hand away from the other’s head, then picked up the scratch paper and the other’s math exam paper and handed them back.
As for why she didn’t continue to explain the later problem types after finishing this derivative function type?
Probably because she sincerely felt it was already hard enough for the other to thoroughly understand just this one problem type in a short time.
She understood the principle of biting off more than you can chew.
“…”
After sending away Situ Ling, who was clinging to her for problem explanation, the girl let out a long sigh.
Subconsciously, she wanted to twirl the pencil in her hand—
Then she realized that while handing over the scratch paper, she had also given away her pencil.
Subconsciously, she wanted to reach out and tap the other’s shoulder to get her pencil back, but seeing the girl staring at the step-by-step analysis she had written with a contemplative expression, the thought that had just arisen was pushed back down.
‘Forget it, it’s just a pencil. After being such good friends for so long, I’ll just give it to her…’
Yin Xiaomeng’s raised hand fell back down.
She didn’t really know what to do.
The bag was still on her lap.
The girl looked down and scanned the books and notebooks inside.
After hesitating for a long time, she pulled out the thick notebook with ‘Error Correction Notebook’ sticker on it.
She flipped through the pages skillfully.
Opening it from the middle, rows of dense small characters filled every corner of the paper.
[No. 1: Prefers torpedoes…]
[…]
Many of the words had a straight diagonal line drawn through them.
Yin Xiaomeng reached out and traced the characters with her finger.
The images stored in her memory began to revive as she read the details in the notebook.
“…”
“Hmm… Let me first write out the persona for No. 6.”
Forcefully interrupting the memories, she touched her nose and flipped the notebook pages further back.
She stopped at a fresh page.
She took a new pencil from the already-taken-out pencil case, then paused and switched to a smoother ballpoint pen.
Out of habit, she unscrewed the cap and drew a small circle in the corner of the paper.
Seeing the evenly colored circular pattern, she nodded imperceptibly and returned her attention to the beginning of the page.
She picked up the pen, then set it down.
[No. 6, acting persona: Dodder flower (dependent personality)]
The pen tip hovered in the air, pausing for a long time.
The girl recalled the rough framework she had thought out in the car, constantly pondering whether that crude framework had any underlying logical conflicts.
‘Dodder flower… In a situation where it can only survive by depending on others, would it actively seek help from outside?’
‘If it really reached the point of needing help, looking at the process of the “seventeen years,” it seems it would have developed a submissive personality. Simply reasons like being forced to marry someone you don’t like or not being able to go to a better school…’
‘Thinking carefully, it still seems a bit untenable.’
Her wrist moved, and most of the text she had just written was crossed out.
‘What about a family that favors sons over daughters… That seems a bit too cliché.’
‘Obviously fake.’
‘…’
‘How about trying to act as a poor special recruit who starts blindly seeking help because of school bullying?’
‘This seems acceptable, at least in terms of “rescue,” it gives the other side plenty of room to maneuver. As long as I don’t describe the experience too excessively, it shouldn’t raise any particular suspicion—’
Of course, the most important thing was that in the school she was currently in, before the new principal took office, there had indeed been cases of special recruits being bullied.
So as long as she added a prefix like ‘the rich kids look out for each other, and even if something happens, it can be suppressed,’ even if the other party actually got suspicious and checked the school’s situation, she would have enough reason to fool them.
Although this might have a less than pleasant impact on the reputation of the classmates she chose and the school…
Well, who cares?
What kind of good person could a classmate she chose be?
‘Okay, I’ll use this for now.’
The ball of the pen rolled, letting ink seep into the paper.
Although the dodder flower setting was temporarily rejected, it wasn’t completely blacked out, meaning the term still existed in Yin Xiaomeng’s selection space.
It was just that she hadn’t thought of a perfect enough script in the short time, so she put the setting aside for now.
“…”
‘This setting will probably be useful again, right?’
‘It will.’
‘If it’s just referring to the two labels of “obedient” and “soft and meek.”‘