Math Is Fun Forum

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?
Thanks a lot in advance

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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 (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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Deon588

Member

Registered: 2011-05-02

Posts: 68

Re: Confusing question

Hi Bob.  I did exactly that up to the point

 
Thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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 (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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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 (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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
Always satisfy the Prime Directive of getting the right answer above all else.