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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

Hi;

[answer removed]

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

[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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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'

I'm not crazy, my mother had me tested.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

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

Children are not defined by school ...........The Fonz

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: 3,648

Which part are you having trouble with analytically?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

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.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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'

I'm not crazy, my mother had me tested.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,548

You're welcome.

Bob

Children are not defined by school ...........The Fonz

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: 103,691

[All comments cleared out to prevent arguments]

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

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.****If it ain't broke, fix it until it is.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

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.****If it ain't broke, fix it until it is.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

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.****If it ain't broke, fix it until it is.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

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: 103,691

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.****If it ain't broke, fix it until it is.**

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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'

I'm not crazy, my mother had me tested.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

I think I asked that.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

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.****If it ain't broke, fix it until it is.**

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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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

bobbym-protection squad

Who is that?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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