u/parallaxastro

https://preview.redd.it/kesbf63g7hth1.png?width=309&format=png&auto=webp&s=e775c6ebf046355acef00a248e13a25cf7ebc907

The graph is stated to be a piecewise equation composed of 3 line segments and a quarter circle with radius 2 centered at (-3, 0).

c > 0 and f(c) = 0.

Essentially, the question is this: what is the value of c such that the average value of the function over the interval -5 <= x <= c is 1/2?

I know that the average value of a function can be found using 1/(b - a) * (F(b) - F(a)), where F(x) is the antiderivative of the function in question and the function is being evaluated over the interval (a, b). Of course, this difference of antiderivatives is equivalent to taking the integral of the function according to the Fundamental Theorem of Calculus.

But I genuinely do not understand how I can possibly find this value of c when I do not have a function to work with. Am I meant to integrate each piece of the function individually based on what I can see in the graph? What am I not understanding?

There were several other questions about this graph that I managed to work through, but this one feels impossible.

Hi.

I used to weigh about 215 pounds at about 5' 11", which was and remains my highest-ever weight. Over the course of about a year and a half and with strict dieting, I lost 65-ish pounds and remained at about 150 for a long time. Then, due to several factors, mainly working often (I work at a restaurant) and eating very rarely, I rapidly lost about 8 pounds. At the time, I looked genuinely skeletal, and my friends and family were concerned that I had an eating disorder. Everyone would constantly remark on how skinny I was, how unreasonable the dietary restrictions I made for myself were, how much weight I'd lost, etcetera. I mean, sure, I looked scary, but it was intoxicating to see how much I'd changed myself. The weight loss had also coincided with a large shift in my life and a self-driven desire to change myself character-wise, and so I perceived the "old me" as a pathetic glutton. Any resemblance I saw to that state made me hate myself.

Jump ahead to the present, and I've been working far less often, and eating more as a result of having more free time. Now, I've gained about 10 pounds from my very lowest weight, and I just want to stop this before it goes any further. Recently, I've restricted myself to eating 1,000 calories a day, but even then I break that every other day and binge myself into an oblivion.

What seems to be unusual about my eating habits is that I can easily restrict myself from eating any particular kind of food that I want. For instance, 10 months ago I decided I would stop eating added sugar of any kind. And I haven't broken that rule! With some small exceptions, I have successfully avoided eating literally any kind of sugar for months.

But for some reason, I don't have the willpower to control the quantity of food I eat. I will eat entire bags of apples, carrots, boxes of strawberries, blueberries, bunches of bananas, loaves of bread, bags of popcorn, thousands of calories worth of nuts, jars of applesauce, etcetera. It's bizarre. I will eat myself into a coma at times. I have tried to stop myself. Nothing works. I track my calories obsessively, and for pretty much nothing. The numbers just keep rising. I try to fast and I break it halfway through the day. I tell myself that I won't give in, and I do anyways. Eating a normal amount of food is impossible. I just fucking love eating.

I managed a 5-day fast, completely spontaneously, when I weighed 30 pounds more! And now, I don't have the willpower to stop eating even for one day. It's absurd.

All this to say, I just need some encouragement. Or support. Or something. I feel that if I know someone else wants me to succeed, I can achieve it. I just need someone to tell me I can do this.

After finishing this game, I found Sunny and his arc to be the most relatable aspects of any work of fiction I've ever experienced.

I'm not a reclusive shut-in, I don't suffer from maladaptive daydreaming, and as far as I know I'm not mentally ill.

But I did do something awful.

Around two years ago, when I was 14, I did something that to this day I consider to be the worst thing I have ever done. I won't name it; I'll leave it up to your imagination. I probably won't tell another person what it was in my lifetime. Suffice it to say, I then thought and now think that it was truly detestable. I'm probably being a bit dramatic, so just in case you're assuming the worst: no, it was not murder. It didn't even affect the people around me. I doubt it would have me arrested, either. But it is, without a doubt, the worst thing I've ever done.

And ever since then, I have been unable to forget, and unable to forgive myself. Every ounce of joy I have had I have secretly thought undeserved. I have constantly thought about my own suicide and all the ways I should physically suffer to atone for it. Like Sunny, what I did was done out of a single instant of pure rage from the mind of a then socially isolated teenager. Like Omori, I have constantly told myself that I do not deserve to live. That I am a disgusting, awful human being who isn't worth the scum on the bottom of other people's shoes. Like Sunny, I have, in fact, become a lot more emotionally withdrawn. Like Omori, I have tried my utmost to shut away the event in my mind. Like the both of them, I loathed myself.

In the time between 14-year-old me and present day, I have improved as a person to a degree I would have never thought possible. My appearance has improved to the point that I'm proud of it instead of hating myself for it, I've achieved so many things academically, I have friend groups and a job and a hundred other things.

But that self-loathing never faded.

Then came OMORI. I had begun playing the game about a year ago (I'd quite liked it), and I'd played about halfway through it before having to stop because my laptop didn't work. Recently, after getting a PC, I was able to play it again, and finish it. The ending of OMORI, the denouement of the narrative ... they're the most cathartic parts of a story I have experienced in my life. Seeing someone else who'd done something similarly awful, who similarly hated himself for it, who was similarly closed-off around other people as a result of it, resonated with me in a way I can't describe. And ... god, his journey to self-acceptance, and his inner battles, his (admittedly imagined) friends' support, they all made me feel as though I were Sunny, in a way, experiencing these things for myself, because so much of what they said and expressed could have been directed towards me.

"Just because you've done a bad thing, doesn't make you a bad person."

That line, which I'd read at 4 AM after a long day and a few short hours of trying to wrap the game up, was just too much. I broke down a bit. I guess I thought, "Really? Can I be forgiven? Am I worthy of living?" I sobbed for a bit. Something just snapped inside of me. It was like I could suddenly face myself. I could be content with the person that I was. When I fought Omori afterwards, I think it was likely the most convicted I've ever been during a fight in a video game. Everything he said was something I had said to myself at one point or another. I suddenly had my own demon, and I was fighting him alongside Sunny's. God, it really was a perfect representation of my own internal struggles.

... And then, afterwards, I felt really strange. It's sort of like ... I've been scrubbed clean of everything I've ever done wrong. It's like I've been completely renewed. I have hope for the future. I want to live. I want to continue. I can forgive myself. I can move on. I can confront life's challenges. I can imagine that I'm worthy of living. I can believe that I am allowed to have happiness.

I don't have a group of friends with high-strung emotional angst to ask forgiveness from or tell the truth to, haha. No one will ever know what it is I've done. But at least I can find a bit of peace, right?

Sorry for rambling, I'm sure you're tired of reading this (if you've bothered, of course), but I just wanted to talk for a bit about this fantastic game.

Take care.