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Tealer
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#1
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#1
Hi there!

This is a really trivial question and I know I must know the method, but I have temporarily forgotten!! Please help - like I say its easy i'm sure!!

differentiate x^3 - 3x^2 + 6x - 2

So that's simple dy/dx = 3x^2 - 6x +6

Then prove there are no turning points. I know a turning pt dy/dx must = 0.

So I set 0 = 3x^2 - 6x +6 To prove this can't be the case, and then I get stuck :|

I know I am being a fool please help!!
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theone
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#2
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#2
(Original post by Tealer)
Hi there!

This is a really trivial question and I know I must know the method, but I have temporarily forgotten!! Please help - like I say its easy i'm sure!!

differentiate x^3 - 3x^2 + 6x - 2

So that's simple dy/dx = 3x^2 - 6x +6

Then prove there are no turning points. I know a turning pt dy/dx must = 0.

So I set 0 = 3x^2 - 6x +6 To prove this can't be the case, and then I get stuck :|

I know I am being a fool please help!!
You want to show for no values of x does 3x^2 - 6x +6 = 0.

Consider this:

3x^2 - 6x +6 = 3(x^2-2x+2) = 3((x-1)^2 + 1) - but this is always greater than 0 for all x so we can not have 3x^2 - 6x +6 = 0, so there are no turning points.
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Tealer
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thanks have some respect
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theone
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(Original post by Tealer)
thanks have some respect
Although it's not worth much, thanks loads, it's the thought that counts
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Tealer
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#5
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Ok the wording of this question has me foxed...

It says prove the following result "A triangle with sides that can be written in the form n^2+1, n^2 - 1 and 2n where n>1 is right angled"
This is very straight forward;

(n^2 +1)^2 = (n^2 -1)^2 + 4n^2
n^4 + 2n^2 + 1 = n^4 + 2n^2 +1

then it goes

"show by means of a counter example that the converse is false"

I do not understand the term converse, converse of what, when n<1 or ?

Many thanks and sorry my respect total is not bigger
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mikesgt2
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(Original post by Tealer)
Ok the wording of this question has me foxed...

It says prove the following result "A triangle with sides that can be written in the form n^2+1, n^2 - 1 and 2n where n>1 is right angled"
This is very straight forward;

(n^2 +1)^2 = (n^2 -1)^2 + 4n^2
n^4 + 2n^2 + 1 = n^4 + 2n^2 +1

then it goes

"show by means of a counter example that the converse is false"

I do not understand the term converse, converse of what, when n<1 or ?

Many thanks and sorry my respect total is not bigger
Would I be right in saying that the converse is:

"A triangle with sides that can be written in the form n^2+1, n^2 - 1 and 2n where n>1 is not right angled"

Then, let n= 2 which is > 1

Therefore, the sides are:

2^2 + 1 = 5
2^2 - 1 = 3
2(2) = 4

Which is a pythagorean tripple, so the trangle is right angled. So, n = 2 is a counter example of the converse statement, ie we have proven the converse to be false.
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theone
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(Original post by mikesgt2)
Would I be right in saying that the converse is:

"A triangle with sides that can be written in the form n^2+1, n^2 - 1 and 2n where n>1 is not right angled"

Then, let n= 2 which is > 1

Therefore, the sides are:

2^2 + 1 = 5
2^2 - 1 = 3
2(2) = 4

Which is a pythagorean tripple, so the trangle is right angled. So, n = 2 is a counter example of the converse statement, ie we have proven the converse to be false.
No this isn't right I don't think.

The converse is that all-right angled triangles can be written in the form
n^2+1, 2n, n^2-1.

A counter example would be any one where the hypotenuse c is not of the form n^2+1.
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mikesgt2
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(Original post by theone)
No this isn't right I don't think.

The converse is that all-right angled triangles can be written in the form
n^2+1, 2n, n^2-1.

A counter example would be any one where the hypotenuse c is not of the form n^2+1.
Oh, maybe you are right. So you are saying that if a statement says 'A implies B', then the converse is 'B implies A.'

For example, if you say 'I hold an umbrela when it rains' then a true statement would be 'It is raining implies I am holding my umbrela'. But the converse 'I am holding my umbrela implies it is raining' is not true because it could be sunny.
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username9816
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#9
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#9
(Original post by mikesgt2)
Oh, maybe you are right. So you are saying that if a statement says 'A implies B', then the converse is 'B implies A.'

For example, if you say 'I hold an umbrela when it rains' then a true statement would be 'It is raining implies I am holding my umbrela'. But the converse 'I am holding my umbrela implies it is raining' is not true because it could be sunny.
i found pure 1 harder than pure 2 !
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nimzy_baby
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#10
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#10
(Original post by bono)
i found pure 1 harder than pure 2 !
hav a look at this one adhsur.

*i am just testing somethin out, please ignore this post*
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