Mathematics - 2017-09-17 (page 2 of 6)

Show that the equation x^5 + 4x^3 - 7x + 14 = 0 has at least one real solution. Use the Intermediate Value Theorem to explain, so how would do this problem without a graphing calculator, it looks like it has no holes so should i try doing the synthetic division

Ted Shifrin

No, @MATH.

Just show it's <0 somewhere and >0 somewhere and explain that it's continuous.

Twink

how can I make this function pass through (2,1)? :S

Ted Shifrin

The shape is not nearly the same, though, @twink. But you can translate on both axes. Review your precalculus. (I have to teach this tomorrow morning.)

Twink

I'm trying to get an approximation of the original graph

not the same graph

Ted Shifrin

1:12 AM

OK, so review precalc. :)

How do you translate vertically (easy)? How do you translate horizontally (slightly harder)?

MATH ASKER

so i would still need it to use synthetic division to try and get it to be a quadratic so i can factor? @TedShifrin

Twink

yeah but I also want it to pass throguh (4,4)

Ted Shifrin

No, no, no, @MATH. You're not going to find the root. You're just using the theorem. Read what I wrote.

Oh, then you're screwed, @twink.

Twink

I just need to add a constant to translate it vertically

Ted Shifrin

You're gonna have to do some stretching, too.

Dodsy

1:13 AM

O.O

Faust

Morning dodsy

Semiclassical

@MATHASKER If you're trying to use synthetic division or some other way of factoring, you're missing the point of the exercise entirely.

Dodsy

late day, faust.

MATH ASKER

yes but to still prove that ones less than zero and the other is greater than zero i have to find the roots and try pluggin them to find y values and see if they are greater or less than zero @TedShifrin

Dodsy

"you're going to have to do some stretching" sounds like a willy wonka quote.

Semiclassical

1:14 AM

You are not asked to find the zero. All you have to show is it exists.

Ted Shifrin

No, no, @MATH, just plug in (intelligently chosen) numbers for $x$.

Faust

pick x =-100 pick x = 100 one value its positive the other its negative there must exist one value between -100 and 100 where it equals 0

Ted Shifrin

too many "it"s in that sentence, @Faust :)

Confusing to a newbie.

Faust

lol

Ted Shifrin

I'm sorta serious.

Use a few nouns..

Faust

1:15 AM

whats a noun?

Ted Shifrin

smacks Faust

Faust

person place or thing?

Ted Shifrin

right

Semiclassical

yep

Ted Shifrin

Part of the chat experience here is learning to be a good teacher

Faust

1:16 AM

so you want me to replace it with function?4

Ted Shifrin

Yes

Dodsy

Im learning to be a good learner :3

ah yes i understand

LOL, OK, Nate.

:S

1:17 AM

But you too have to do your share of helping.

Dodsy

Ah, one day.

Ted Shifrin

That's how you become better at math. That's seriously one reason I did so well on GREs ... was because I'd spent so much time helping/teaching people calculus and such.

Faust

he helped me drink some beer yesterday that counts right?

Ted Shifrin

Um, no.

Dodsy

haha

you make me sound like a country bumpkin, Faust.

Semiclassical

1:18 AM

that's a bonding experience, not a teaching one :P

Dodsy

@TedShifrin that's true.

Twink

can all Bezier curves be represented by a formula?

Ted Shifrin

hell no

3

Faust

@TedShifrin lol

Twink

then the formula I'm looking for may not exist

Ted Shifrin

1:19 AM

although they often use cubic splines (gluing different cubics together)

right

Semiclassical

not in the sense of $y=f(x)$

Ted Shifrin

when I click and drag, I don't have cubic splines

Dodsy

@TedShifrin my prof answered me

MATH ASKER

ight i chose -4 and got -1294 so than should i choose another number?

Ted Shifrin

yup

Dodsy

1:20 AM

and confirmed what everyone said here.

Semiclassical

I would say there's a formula in the sense of Bezier curves being piecewise parametric

Faust

@MATHASKER try a positive one

Semiclassical

but that's not a useful characterization for the present purpose

Ted Shifrin

Semi, I think they're piecewise-cubic, but you don't always get splines when you click and drag in Illustrator.

MATH ASKER

tried positive 4 and got 1266

Semiclassical

1:21 AM

hmm, fair

Faust

now what does the IVT say?

MATH ASKER

that for a negative x there must be a y and for a positive x there must be a y?...

Faust

no

Ted Shifrin

Reread what I typed up there ^^^^^

Semiclassical

Don't go into vagueries. Be specific.

Ted Shifrin

1:22 AM

Damn, everyone's hanging up on poor @MATH, but it's good for him.

Semiclassical

What does the IVT state, if you have $a=-4$ and $b=4$?

it builds character? :P

Faust

it says that there is some value c in the domain (-4,4) where f(c)= ?

Dodsy

Weird question but does $(x-3)^{\frac{1}{3}} = \sqrt[3]{(x-3)}$

Semiclassical

do \sqrt[3]{}

Dodsy

thanks

Semiclassical

1:24 AM

np

MATH ASKER

one from my notes said that f(c) = (f(a), f(b))

Dodsy

that's equal though right?

Ted Shifrin

That's crap, @MATHASKER.

Dodsy

or is my notation off.

Ted Shifrin

Remember I told you what you originally typed was garbage?

Semiclassical

1:24 AM

I'd say that's fine, @dodsy

Dodsy

thanks semi.

Ted Shifrin

Yes, for any real number $a$, $a^{1/3} = \root3\of a$.

Remember what $a^{m/n}$ means.

Semiclassical

The only place where it could be problematic is for complex values, and well

MATH ASKER

oh true, i guess i got the notes wrong let me see what you wrote gotta scorll up

Ted Shifrin

For complex, it's all multivalued. Note I said real.

Semiclassical

1:25 AM

complex isn't really relevant

Twink

@TedShifrin why do you like to be mean?

Dodsy

!?

oh this guy again rolls eyes

Ted Shifrin

I don't think I've been mean. I'm direct.

Faust

@MATHASKER what value would like f(c) to equal ? that would help you with the roots of the function?

Ted Shifrin

Don't stir up trouble, twink.

I don't pamper students, but I'm not mean.

Twink

1:26 AM

It's mean to tell someone what he said is garbage

Ted Shifrin

It made no sense (which is what I typed the first time).

MATH ASKER

so i chose like -1 which is in between -4 and 4

Dodsy

Ted, in my opinion, it isn't worth it.

Twink

but that's rude

MATH ASKER

and see if there is a value for that?

Faust

1:26 AM

@MATHASKER what does it mean for something to be a root of a function

Ted Shifrin

Well, you won't get good at math if I tell you you're wonderful when you're not.

Dodsy

No I mean, if it was me, I wouldn't engage "Twink".

MATH ASKER

that when you plug that number in you get zero as an answer

Ted Shifrin

I know, Nate. We're old "friends."

Faust

ok good!

Twink

1:27 AM

and he won't get good at math telling him that what he said is garbage

Dodsy

Oh haha.

Faust

so you would like f(c)=0 !

for some c

Twink

and remember there's always people better than one

Ted Shifrin

@twink: Over my long teaching career, I did have some students who did not like me. But 95% liked me a lot and probably 50% took multiple courses from me.

I don't need you lecturing to me. If you don't like me, then ignore me.

Faust

now the IVT tells you that there is some c between -4 and 4 such that f(c)=0

Ted Shifrin

1:28 AM

But I'm proud that Faust is taking over and doing a great job.

MATH ASKER

yes @Faust

Twink

teachers learn from the students too

Ted Shifrin

sometimes

Faust

so the IVT tells you that there is some root in there which was what your original question was asking you to show

Ted Shifrin

it's odd that you like to pick at me because I'm openly gay.

Twink

1:29 AM

but not when you're arrogant

Ted Shifrin

It's not arrogant to say that something makes no sense. But I get your point. Let's drop it.

Twink

LOL who's talking about sexuality?

Dodsy

>_>

Ted Shifrin

You have made huge fusses in here, twink. So cut it out.

Twink

if you say so..

Dodsy

1:30 AM

So, what's up for tomorrow, Ted?

Ted Shifrin

rolls 9 3/4 eyes

MATH ASKER

so do like try to pick a number between those two and see which one equals to zero @Faust

Ted Shifrin

Teaching functions, Nate :)

Dodsy

Teaching?

Nice!

Ted Shifrin

Yeah, I'm teaching a class every Sunday to math geeks ;)

Twink

1:31 AM

and going to the gay club later

Balarka Sen

It's not rude to tell someone that what they're saying is garbage. Pretty typical in the math community. If someone takes that as insult, get over it.

Dodsy

sighhhh.

Balarka Sen

It's a critique of the argument, not of the person

Faust

@MATHASKER you simply can show the calculations for f(-4) and f(4) then say by the IVT a root c exists between -4 and 4 such that f(c) =0

and your done

Ted Shifrin

@Dodsy: It's a small class, but so far some of them seem really smart.

Dodsy

1:32 AM

honestly, today somebody told me something I said was nonsense and it saved me a lot of embarrassment, because I would've handed in nonsense.

Ted Shifrin

I tried for 2 years to volunteer tutor at-risk kids, but that's harder than getting a paid job. Probably twink thinks I'm not qualified.

Dodsy

@TedShifrin That's great! I'm sure the students enjoy it just as much as you do. :) I find that (assofar) professors that show a great interest in what they teach seem to be more fun to listen to.

Faust

@MATHASKER you were simply asked to show that a root existed not what the actual root is as a number

Ted Shifrin

Nate, I think you tend to learn more if the teacher wants you to.

Dodsy

Me personally? Or in general?

Ted Shifrin

1:33 AM

@Faust: I think the hard part of IVT is that it's just vague existence, and students expect that a precise answer is expected.

In general, Nate.

Dodsy

I think both apply, but trying to discern your meaning.

Ah, I see. I agree.

MATH ASKER

oh true, @Faust ight thanks guys i guess i was misinterpeting what my teacher was teaching thats why i made it so complicated

Twink

@TedShifrin you are one of the most qualified people here, but also one of the most arrogants

Ted Shifrin

Sure thing, @MATH. It's a new thing to have theorems/statements like that.

And you're being so constructive, twink.

MATH ASKER

he wrote something like c(a,b) f(c) = f(a),f(b)) and i just copied it down cause i wasnt paying attention

Faust

1:35 AM

@TedShifrin well it is arguably the first time where you wave your hands around for awhile and then say a solution exists but i haven't a inclination what it is. at least it was the first time for me in mathematics

Ted Shifrin

I think he wrote $\in$ without explaining it, @MATH.

So you wrote =

Faust

thats why i avoided element and domain and range

Ted Shifrin

Yes, Faust, you did superbly.

MATH ASKER

maybe, i might go to my teacher and try to clear it up a bit more, lol i did this in pre-calc, thats why it was confusing me lol

Faust

i know that confused the crap out of me in calc I

Ted Shifrin

1:36 AM

I tried to say "between" and stuff earlier.

Aren't you supposed to be asleep, Jasper?

Faust

woot woot jasper in dah house

Dodsy

Jasps

Jasper

I went to see SBA's calculus class.

Ted Shifrin

Just don't leave out an "s" there, Nate.

Oh, how's he doing?

Jasper

I just tried to contribute a little here and there.

Dodsy

1:38 AM

lmfao.

Faust

@MATHASKER a teachers Office Hours are more important than the actual class imho

Ted Shifrin

Both are important.

Jasper

There weren't many students, and it started a couple hours late.

Dodsy

I am shaking my head @TedShifrin

Ted Shifrin

A couple of hours late!!

I suppose that's ok, Nate.

Jasper

1:39 AM

I don't know whether the students actually understood or not, because there wasn't time for tests.

But we just discussed the epsilon delta definition, that's about it.

Ted Shifrin

It's really tough for a youngster to be in charge of an on-line class with no teaching experience and little mathematical experience. But I applaud him for trying.

I hope he'll ask us for help/advice if he needs to.

I think the whole idea is crazy, personally ...

Jasper

Yeah.

Ted Shifrin

Except he isn't, Nate.

Dodsy

no haha, I know

Ted Shifrin

Damn Scientologist.

Twink

1:41 AM

@Dodsy why are you stalking me?

Dodsy

just found that part of the transcript funny.

I am not, sir.

Twink

yes, you are, sir

Ted Shifrin

I think I'm going to cook dinner. Anyone who wants to drop by is welcome.

Most I know don't.

Twink

now I know one who does

Dodsy

@Twink No, I overheard you talking to Ted before and was looking for that conversation, not stalking you.

I'd have no benefit to stalking you, Twink.

@TedShifrin enjoy your dinner!

Twink

1:43 AM

sure

Semiclassical

too much paranoia in this chat

Dodsy

yes.

Twink

I don't agree

Dodsy

believe what you like :)

Jasper

Hi @Twink, lol

Balarka Sen

1:44 AM

the chat needs to be rid of the trolls and the dramatists

Dodsy

@BalarkaSen I have a feeling that I would be eradicated O.O

Twink

I don't care what you feel

Dodsy

I didn't mean to offend you, Twink.

just thought the transcript was funny.

Twink

you didn't, you need much more to offend me

Jasper

What is going on?

Twink

1:46 AM

hi @Jasper

Semiclassical

@Jasper not a damn clue

Twink

I think Dodsy has a crisis

Jasper

LOL

(removed)

Dodsy

I had to remove it sounded too ridiculous.

:(

Twink

:)

Jasper

1:50 AM

I now have a suspicion that Dodsy is Twink...

Dodsy

you are $\iff$ mean

Wouldn't that be really weird?

Twink

Jasper now you're having hallucinations

Jasper

LOL

Twink

you're getting worse and worse :(

Dodsy

Hey @LeakyNun

Twink

1:51 AM

you need help

Jasper

But how can you two respond to each other so quickly?

Leaky Nun

hi

Dodsy

idk @Jasper I didn't think it was that quick.

Twink

typing fast?

Dodsy

no, I am a very slow typer.

Jasper

1:52 AM

Hmm, then I guess you two can be good friends. You have a lot of chemistry, lol.

Dodsy

:o

Balarka Sen

This chat right now

Twink

I prefer prostate cancer

Dodsy

@BalarkaSen what's that comment

Faust

thats defintly terriffing

Dodsy

1:53 AM

by kieran

Jasper

@Twink I once had it examined. It was a weird sensation.

Dodsy

@Jasper be careful, you're dating yourself.

Balarka Sen

@Dodsy loool i never noticed that comment

Jasper

@Twink Nope, just a weird sensation, lol.

Twink

was it a nice sensation?

Dodsy

1:55 AM

@Twink not sure if these are appropriate questions, Twink.

Jasper

Change of topic then, lol.

So what brand of coffee do you guys like?

Dodsy

Tim Hortons, of course.

Jasper

These days I just get those in a packet and add hot water.

Dodsy

Tim hortons coffee?

They have timmies where you live, Jasp?

Jasper

I just drink some brandless one, lol.

Dodsy

1:56 AM

oh I see.

Jasper

Hmm, I don't think I have seen timmies in Antarctica.

Twink

@Jasper are you still crazy?

Dodsy

D:

Antarctica!?

Twink, seriously bud??

Jasper

@Twink Yes, I am still trying to get better. I hope I can make it soon. Pray for me.

Twink

I can't

I don't believe in god

Jasper

1:58 AM

Pray means fervent hope that sends EM waves across the universe.

You don't need to believe in any god for that.

Twink

I don't believe in sending waves

Jasper

OK then

Dodsy

Twink, how about you just believe in being nice to others and sensitive to their feelings?

Twink

but it's possible that you'll be crazy for the rest of your life

Jasper

Well, I have hope.

Twink

1:59 AM

I just said it's possible

Dodsy

First of all, "crazy" is offensive.

Jasper

@Dodsy What's your favourite brand of beer again?

Transcript for

$Mathematics$ Mathematics