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## #1 2011-09-28 09:31:35

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

### Confusing question

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?

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## #2 2011-09-28 09:56:48

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

### Re: Confusing question

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

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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## #3 2011-09-28 11:00:09

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

### Re: Confusing question

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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## #4 2011-09-28 13:03:09

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

### Re: Confusing question

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)

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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## #5 2011-09-28 19:33:41

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

### Re: Confusing question

Hi Bob.  I did exactly that up to the point

Thanks

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## #6 2011-09-28 19:51:32

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

### Re: Confusing question

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)

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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## #7 2011-09-28 22:02:29

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

### Re: Confusing question

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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## #8 2011-09-29 03:14:31

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,689

### Re: Confusing question

Hi Deon588;

Yes, there is a way using just algebra.

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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## #9 2011-09-29 03:59:46

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

### Re: Confusing question

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)

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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## #10 2011-09-29 04:13:34

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

### Re: Confusing question

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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## #11 2011-09-29 04:16:23

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,689

### Re: Confusing question

Hi Deon588;

Your welcome. What year are you in?

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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