More Maths Help

SoSolid · 7 May 2006 at 20:52

Right now this question should be easy but i am unsure as to what it is exactly asking for, I know how to complete the square but how should i display my answer, please help!

By completing the square, or by quoting the known facts in relation to a quadratic function, show that for all x E R

F(x) = -3x^2 + 6x -9 < -6

Seft · 7 May 2006 at 20:55

solve for the first derivative being zero. Input your solution then check that it is a maximum.

SoSolid · 7 May 2006 at 20:58

This is a completing the square question not differentiation one. Thanks any how though.

PinkPig · 7 May 2006 at 21:13

SoSolid said:
This is a completing the square question not differentiation one. Thanks any how though.

Well, says who? I appreciate if it's under a "completing the square" heading, then I suppose you ought to do it that way, but in any moderately decent exam or project then any valid method will be accepted.

If you want to complete the square, I suppose:

say:
f(x) = - (x^2 - 2x + 3) = - [(x-1)^2 + 2]
maximum value occurs x = 2, f(X) = -2
so F(x) = 3f(x) has maximum value at f(x) = -6
so F(x) < -6

would be a decent way of writing it

Or, differentiating:

F'(x) = -6x + 6
F'(x) = 0 => x = 1 => F(x) = -6

F''(1) = -6 < 0 , so this is a maximum point.

so F(x) < -6

DaveyD · 7 May 2006 at 21:13

Unless I've read it wrong

from

-3x^2 + 6x -9 < -6

Re-arrange to make one side 0, then work from there.

SoSolid · 7 May 2006 at 21:15

PinkPig said:
Well, says who? I appreciate if it's under a "completing the square" heading, then I suppose you ought to do it that way, but in any moderately decent exam or project then any valid method will be accepted.

chill out.

PinkPig · 7 May 2006 at 21:16

SoSolid said:
chill out.

Nothing to chill out about, just pointing out that there's nothing wrong with differentiation - in fact it would probably count as "easier", since completing the square needs you to spot something in particular.

daz · 7 May 2006 at 21:18

-3x^2 + 6x -9 < -6

0 < 3x^2 - 6x + 3

0 < x^2 - 2x + 1

0 < (x-1)^2

Meatball · 7 May 2006 at 21:19

Ok sorry to steal your post but I'm revising GCSE chemistry and need help with answering a chemistry question. I've made two threads today so I thought I would just use this one since its kind of the same subject.

How in gods earth do I answer this? I can never remember.

PinkPig · 7 May 2006 at 21:19

daz, that's a horrible way to work it out. You're trying to show that the first line is correct, not show something else that follows from it.

DaveyD · 7 May 2006 at 21:19

daz said:
-3x^2 + 6x -9 < -6

0 < 3x^2 - 6x + 3

0 < x^2 - 2x + 1

0 < (x-1)^2

Could have let him do it on his own after a hint to be honest

PinkPig · 7 May 2006 at 21:23

-White-Knight- said:
How in gods earth do I answer this? I can never remember.

That's a very easy question.
You can find the relative masses of each part of the equation:
ie C8H18 is 12*8 + 18, and so on.
So you will find something like x units of the fuel gives y units of CO2, then scale it up to 114g of the petrol.
And it's not really got much to do with the previous question

I wish I didn't procrastinate by answering these questions when I have impossible maths revision of my own to be doing!

Meatball · 7 May 2006 at 21:24

PinkPig said:
That's a very easy question.
You can find the relative masses of each part of the equation:
ie C8H18 is 12*8 + 18, and so on.
So you will find something like x units of the fuel gives y units of CO2, then scale it up to 114g of the petrol.
And it's not really got much to do with the previous question
I wish I didn't procrastinate by answering these questions when I have impossible maths revision of my own to be doing!

Oh god, I found it hard :O. Thanks for the help. It was kind of the same, revision and helping with questions but thanks. I'll go shut up and practice now.