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#1 2014-05-16 18:14:23

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

How do I get back the polynomial?

Let f(x) = a x^3 + b x^2 + c x + d

You are given that:

1. f(3) = 5
2. f(-1) = 9
3. f(x) has its minimum at x = 0
4. f'(x) has its maximum at x = 1

How can I get back a,b,c,d?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2014-05-16 19:46:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Hi;

[answer removed]


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-05-16 21:09:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

How do I do this?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2014-05-16 21:16:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

[due to arguments that have fanned out to other threads, this answer is removed]


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#5 2014-05-17 00:35:44

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

Test what?

Thanks for the code.

What kind of a combinatoricist notes down all his opinions in a serialised fashion?!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2014-05-17 00:40:00

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,336

Re: How do I get back the polynomial?

hi Agnishom,

By 'hand' answer:

minimum at 0 => c = 0

maximum at x = 1 => 6a + 2b = 0 => b = -3a  .................(1)

subtracting

substituting (1) gives

Who needs are CAS?  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2014-05-17 00:41:15

ShivamS
Member
Registered: 2011-02-07
Posts: 3,523

Re: How do I get back the polynomial?

Which part are you having trouble with analytically?

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#8 2014-05-17 00:42:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Hi Agnishom;

I gave you the equations.

What kind of a combinatoricist notes down all his opinions in a serialised fashion?!

A smart one.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#9 2014-05-17 00:52:42

ShivamS
Member
Registered: 2011-02-07
Posts: 3,523

Re: How do I get back the polynomial?

I cross-posted with bob bundy, never mind.

He's right, who needs a CAS smile

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#10 2014-05-17 00:56:13

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

Bob: Thank You smile

who needs a CAS?

That combinatoricist from Vegas does.

Bobbym: Have you serialises your opinions like him?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#11 2014-05-17 00:59:57

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,336

Re: How do I get back the polynomial?

You're welcome.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2014-05-17 01:02:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

[All comments cleared out to prevent arguments]


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#13 2014-05-17 01:06:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

I was joking, of course.

The next thinks I am not a bobbymist..


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#14 2014-05-17 01:10:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Bobbym: Have you serialises your opinions like him?

Another serious misconception. I have no opinions. All my stuff was given to me by some top ranked mathematicians. Some I can understand and use, others I just get wrong. I have never really discovered anything new in my entire life.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#15 2014-05-17 01:14:44

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

I know that you have not serialised your opinions, not even quotes. That is why I am recording your quotes for the betterment of the society in near future.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#16 2014-05-17 01:23:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Hmmm, you did not read the last post. Aping RF,HW or DZ is not an opinion really. Even when I thought I had something original I always found that they got there first! You are recording their words and concepts as best as I understand them.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#17 2014-05-17 02:33:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

Hi;

I was joking. I hope that you understand.

Also, I have used the CAS approach to solve the problem. I am truly grateful of the efforts your put up do carry forward the message of great mathematicians.

I hope you do not get me wrong..


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#18 2014-05-17 02:36:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

I only wish to prevent arguments. I have removed the controversial part of the thread.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#19 2014-05-17 02:37:44

ShivamS
Member
Registered: 2011-02-07
Posts: 3,523

Re: How do I get back the polynomial?

bobbym wrote:

[All comments cleared out to prevent arguments]

I think bobbym has become too serious.

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#20 2014-05-17 02:43:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Why do you think that? It is my job to keep the forum running smoothly, the answer to one question takes second place to that.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#21 2014-05-17 02:45:34

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

The solution was a nice one. Everyone likes it.

Agnishom's post brought in the controversy.

The following is what started it all:

Agnishom wrote:

who needs a CAS?

That combinatoricist from Vegas does.

Bobbym: Have you serialises your opinions like him?

The next should have removed it instead


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#22 2014-05-17 02:46:39

ShivamS
Member
Registered: 2011-02-07
Posts: 3,523

Re: How do I get back the polynomial?

I think I asked that.

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#23 2014-05-17 02:47:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

Hmmm, sorry I already made the decision. Can not be undone, so why discuss it?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#24 2014-05-17 02:48:44

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,251
Website

Re: How do I get back the polynomial?

But the bobbym-protection squad is planning to arrest me for answering the question...


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Offline

#25 2014-05-17 02:49:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,338

Re: How do I get back the polynomial?

bobbym-protection squad

Who is that?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

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