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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi. I am a bit confused with this question the question is "Find the coordinates of M when BA is a maximum" Should I subtract the straight line from the parabola and then

I don't understand how BA has any effect on M? Doesn't M just stay where it is on the x-axis?Thanks a lot in advance

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi Deon588,

Have you got a, b and c yet?

I'll assume yes.

That fixes the parabola (ie. there's only one answer) and the line is obviously unique.

But B can move about on the parabola and so that means M moves too.

I'd call M (x,0) and write the coordinates of B and A in terms of this.

Then you write an expression for BA in terms of x, differentiate, and hence get the maximum.

I'd better go and get a piece of paper and try it out.

Bob

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

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi Bob I have the parabola and lines equations. So to find the maximum I subtracted the line's equation from the parabola's equation but from here i'm not sure.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi Deon588

I got a = -2 b = -4 and c = 0

Then for the points:

So

So you need

Can you take over from here?

Bob

*Last edited by bob bundy (2011-09-28 13:07:23)*

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

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi Bob. I did exactly that up to the point

Thanks

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi Deon588

d(BA)/dx is a special notation used in the differential calculus.

It gives you a way of finding the maximum value of an expression (amongst many, many uses!).

It's too big a topic to start in answer to the question, if you haven't met it before.

But don't worry. As the expression

is a quadratic there's another way to get the maximum value.

I've put the graph below. As you can see it does have a maximum value. Would you be able to work out the x, at this point?

Bob

*Last edited by bob bundy (2011-09-28 19:53:04)*

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

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Hi Bob. Differential calculus is not part of my course this year at all. So I can find x either by completing the square or

?If i'm asking for help too much lately please let me know. I have exams in 3 weeks so trying to get everything cleared up before the exam.

Thanks

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi Deon588;

Yes, there is a way using just algebra.

**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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

hi Deon588

will do nicely.

(But using the 'a' and 'b' from the new quadratic, of course.)

Bob

*Last edited by bob bundy (2011-09-29 04:00:38)*

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**Deon588****Member**- Registered: 2011-05-02
- Posts: 68

Thanks a lot Bob and Bobbym. I have done this many times before but the way the question was written confused me a bit

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi Deon588;

Your welcome. What year are you in?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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