View Full Version : Weird thing I found in Calculus

slooksterpsv

October 3rd, 2010, 04:57 AM

Ok so this is weird, but for an equation where:

f(x) = ax^2+bx+c

|(f(x+1)-f'(x+1))|-|(f(x)-f'(x))|=f''(x)

I'm guessing this is already known? I just thought it was cool cause here's how I figured it out:

f(x) = x^2 + 2x

f'(x) = 2x + 2

f(1) = 1 + 2 = 3

f'(1) = 2 + 2 = 4

f(1)-f'(1)= -1

f(2) = 4 + 4 = 8

f'(2) = 4 + 2 = 6

f(2)-f'(2) = 2

f(3) = 9 + 6 = 15

f'(3) = 6 + 2 = 8

f(3)-f'(3) = 7

|-1 - 2| = 3

| 2 - 7| = 5

| 3 - 5| = 2

f''(x) = 2

So overall, this proves that:

|(f(x+1)-f'(x+1))|-|(f(x)-f'(x))|=f''(x)=2a

Sorry just thought it was cool lol

nmaster

October 3rd, 2010, 05:18 AM

that's not a proof of anything. you chose a single polynomial and then showed that your statement was true at a single point.

you need to take some classes or study some good books on analysis if you want to be able to make (and prove) claims like this.

Troublegum

October 3rd, 2010, 05:27 AM

First thing: that's not a proof.

And second: I don't know how you got the idea, but your theory is wrong. That equation is simply false.

It justs works for that specific function you've chosen.

Lightstar

October 3rd, 2010, 05:40 AM

"if a gorilla were to step on a flower then the goat in the forest would prove that reading what was said is just not the same as a book in the refrigerator." - Skim Bowie

Frank_Schley

October 3rd, 2010, 05:46 AM

if f[x] = ax^2 + bx + c, then

Abs[f[x+1] - f'[x+1]] -Abs[f[x]-f'[x]]=

-Abs[-b + c - 2 a x + b x + a x^2] +

Abs[-b + c - 2 a (1 + x) + b (1 + x) + a (1 + x)^2], which might equal 2 but doesn't have to.

Still a cool example though.

ubunterooster

October 3rd, 2010, 07:20 AM

I still like

If (X) x (X) = (Y),

then (X+1) x (X-1) = (Y-1),

therefore (X-2) x (X+2) = (Y-4)...

Tibuda

October 3rd, 2010, 11:48 AM

induction is not proof...

GeneralZod

October 3rd, 2010, 11:55 AM

induction is not proof...

Before anyone pounces: I'm sure he means http://en.wikipedia.org/wiki/Inductive_reasoning, not http://en.wikipedia.org/wiki/Mathematical_induction :)

cap10Ibraim

October 3rd, 2010, 03:44 PM

Before anyone pounces: I'm sure he means http://en.wikipedia.org/wiki/Inductive_reasoning, not http://en.wikipedia.org/wiki/Mathematical_induction :)

okay , now that makes sense becuz we do use induction to prove some propositions

Windows Nerd

October 3rd, 2010, 05:37 PM

I still like

If (X) x (X) = (Y),

then (X+1) x (X-1) = (Y-1),

therefore (X-2) x (X+2) = (Y-4)...

I still like the mathematical proof that girls are indeed, evil:

First we state that girls require time and money:

girls = time x money

Edit: yes, the logic of the written statement should translate to "girls = time + money, but for the sake of the joke, let it be.

As we all know, "time is money"

time = money

Therefore,

girls = money x money = (money)^2

And because "money is the root of all evil"

money = sqrt(evil)

Therefore:

girls = (sqrt(evil))^2

Then we are forced to conclude that:

girls = evil

Edit: I also found that someone one the site where I stumbled across this joke that someone added to the humor:

"Jim Garrigues" says:

I have a suggestion for the proof that girls = evil.

I believe that when you say:

x = (sqrt(y))^2

that you can only say that

x = |y| (absolute value of y)

therefore,

if girls=(sqrt(evil))^2

then girls=|evil|

or girls are "absolute" evil!

-Jim

Windows Nerd

October 3rd, 2010, 05:47 PM

okay , now that makes sense becuz we do use induction to prove some propositions

Science is all technically inductive reasoning. According to my physics teacher.

Linye

October 3rd, 2010, 06:31 PM

Stupid calculus.

JDShu

October 3rd, 2010, 09:32 PM

Science is all technically inductive reasoning. According to my physics teacher.

Yep, that's why Science is technically not proven.

JDShu

October 3rd, 2010, 09:34 PM

And because "money is the root of all evil"

Another flaw is that its the "love of money" which is the root of all evil.

forrestcupp

October 3rd, 2010, 10:23 PM

This thread is proof that no matter how smart you think you are, there are always at least 10 people at hand that are going to put you down and make you look completely stupid. And it doesn't matter what the subject is or even how much of an expert you are on that subject.

JDShu

October 3rd, 2010, 10:36 PM

This thread is proof that no matter how smart you think you are, there are always at least 10 people at hand that are going to put you down and make you look completely stupid. And it doesn't matter what the subject is or even how much of an expert you are on that subject.

Indeed, but that's how we learn :D

Linye

October 4th, 2010, 01:06 AM

This thread is proof that no matter how smart you think you are, there are always at least 10 people at hand that are going to put you down and make you look completely stupid. And it doesn't matter what the subject is or even how much of an expert you are on that subject.

Yep; there's always someone better than you.

standingwave

October 4th, 2010, 03:50 AM

16/64 = 1/4 (cancel the sixes)

19/95 = 1/5 (cancel the nines)

26/65 = 2/5 (cancel the sixes)

49/98 = 4/8 (cancel the nines)

Whenever you have nines or sixes in both the numerator and denominator, just cancel those suckers out!

QED

renkinjutsu

October 4th, 2010, 04:37 AM

Personally, I believe there is no other genius quite like Randall Munroe..

http://xkcd.com/759/

standingwave

October 4th, 2010, 05:39 AM

http://www.youtube.com/watch?v=rLprXHbn19I

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