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# Maths C3 - Harmonic Identities - Finding Max and Min Values... HELP??? watch

1. (Original post by RDKGames)
Seems right.
Sorry I know you're against the use of quadrant diagrams but I seem to make less mistakes this way even though it takes a little longer. The good thing is I think I'm starting to understand Harmonic Identity questions involving Min or Max values
2. Just want to thank you guys (Kevin De Bruyne, notnek and RDKGames) for helping me out and being patient with me with a topic that I always seemed to struggle with! Hopefully it makes more sense to me from now on.
3. (Original post by notnek)
So do you now know where comes from? I'm asking because this hasn't been explained to you since you said that you don't know where it comes from.
(Original post by Philip-flop)
Just want to thank you guys (Kevin De Bruyne, notnek and RDKGames) for helping me out and being patient with me with a topic that I always seemed to struggle with! Hopefully it makes more sense to me from now on.
Just gonna say it in case he doesn't...

To minimise , you need to minimise . Clearly the minimum value of this is 0, and it is achieved when (because if it were equal anything other than 0, the square of it would not be 0)
4. (Original post by RDKGames)
Just gonna say it in case he doesn't...

To minimise , you need to minimise . Clearly the minimum value of this is 0, and it is achieved when (because if it were equal anything other than 0, the square of it would not be 0)
Yeah so the expression is...

And to find it's minimum value we let the because we want it to give the smallest possible value for this minimum, thus giving...

Right?
5. (Original post by Philip-flop)
Yeah so the expression is...

And to find it's minimum value we let the because we want it to give the smallest possible value for this minimum, thus giving...

Right?
You're not wrong, but I don't like the way your argument goes from to , rather than the other way round.

The minimum value of is clearly -1 when minimised but that would mean is 1.

But if you start your argument by minimising , so it is 0, then is 0.
6. (Original post by RDKGames)
You're not wrong, but I don't like the way your argument goes from to , rather than the other way round.

The minimum value of is clearly -1 when minimised but that would mean is 1.

But if you start your argument by minimising , so it is 0, then is 0.
Oh I see, so it's better to expand the bracket first so...

Becomes...

So for the minimum value

Therefore min value of

Is that the way I should do it?
7. (Original post by Philip-flop)
Oh I see, so it's better to expand the bracket first so...

Becomes...

So for the minimum value

Therefore min value of

Is that the way I should do it?
I guess, there's nothing wrong with it... but again, you go from to when it makes more sense to do it the other way around since is dependent on , so you want THIS minimised which means and this IMPLIES

Maybe I'm just being pedantic here and I doubt you would lose ANY marks for this, but to minimise you should notice that first saying "min of " then going onto "min of " doesn't flow very nicely because the min of is -1 (not 0 as you claim) and this value does NOT minimise . Whereas if you went from saying first "min of " (which is 0 and minimised H first of all) IMPLIES "min of " (which is also 0 as a result) then it makes sense. It's more logical this way.

All in all, this bit just lacks argument as to WHY is picked as 0 and not its minimum which would be -1.

(Original post by Philip-flop)

So for the minimum value
8. Philip-flop Just adding to what RDKGames said here:
All in all, this bit just lacks argument as to WHY is picked as 0 and not its minimum which would be -1.
A large percentage of students would think that should be -1 to have a minimum because this is what they're used to in most exam questions. It's important that you understand why in this case it should be 0.
9. (Original post by RDKGames)
I guess, there's nothing wrong with it... but again, you go from to when it makes more sense to do it the other way around since is dependent on , so you want THIS minimised which means and this IMPLIES

Maybe I'm just being pedantic here and I doubt you would lose ANY marks for this, but to minimise you should notice that first saying "min of " then going onto "min of " doesn't flow very nicely because the min of is -1 (not 0 as you claim) and this value does NOT minimise . Whereas if you went from saying first "min of " (which is 0 and minimised H first of all) IMPLIES "min of " (which is also 0 as a result) then it makes sense. It's more logical this way.

All in all, this bit just lacks argument as to WHY is picked as 0 and not its minimum which would be -1.
I don't think I completely follow I don't even know what the minimum of is

All I can see is that it has to be since if it is -1 we would get which is a bigger number than if we have it as 0, therefore which is the smallest possible value we can make for the minimum.
10. (Original post by Philip-flop)
I don't think I completely follow I don't even know what the minimum of is
You REALLY need to know that the square of anything that can be 0, IS 0...
11. (Original post by Philip-flop)
I don't think I completely follow I don't even know what the minimum of is

All I can see is that it has to be since if it is -1 we would get which is a bigger number than if we have it as 0, therefore which is the smallest possible value we can make for the minimum.
To me this looks like you understand.

The minimum of is -1 but the minimum of is 0 for the reasons you say above.

In this case you have and the minmum of this will be the same as the minimum of .
12. (Original post by notnek)
Philip-flop Just adding to what RDKGames said here:

A large percentage of students would think that should be -1 to have a minimum because this is what they're used to in most exam questions. It's important that you understand why in this case it should be 0.
I think that's why I would normally slip up on these!

(Original post by RDKGames)
You REALLY need to know that the square of anything that can be 0, IS 0...
Yeah I know that always gives zero but I've never really thought about actually relating that fact to graphs. But I understand why a parabola like has a minimum point at
13. (Original post by notnek)
To me this looks like you understand.

The minimum of is -1 but the minimum of is 0 for the reasons you say above.

In this case you have and the minmum of this will be the same as the minimum of .
Yeah that's the way I saw it. But like RDKGames is saying I probably should have known that a graph like has a minimum value of zero so due to the outputs when squaring numbers. It's almost like comparing it to

But I feel like I will slip up more say if I was to adopt this approach to a fractional type Harmonic Identities question
14. Wow, I've never come across a question like this before.

Part(c) I actually had no idea what to do, thank god for exam solutions though! Hopefully I'll be prepared if a similar question appears in the Edexcel C3 paper this summer!

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