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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

[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.**

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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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

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?

Bob

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

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

Which part are you having trouble with analytically?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

I cross-posted with bob bundy, never mind.

He's right, who needs a CAS

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Bob: Thank You

who needs a CAS?

That combinatoricist from Vegas does.

Bobbym: Have you serialises your opinions like him?

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

You're welcome.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

[All comments cleared out to prevent arguments]

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I was joking, of course.

The next thinks I am not a bobbymist..

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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.

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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..

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

bobbym wrote:

[All comments cleared out to prevent arguments]

I think bobbym has become too serious.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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

'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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,528

I think I asked that.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

bobbym-protection squad

Who is that?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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