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How to find the x-coordinates of a minimum turning point P?

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1. So I did (a) & (b) but don't know how to solve (c)
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So I did (a) & (b) but don't know how to solve (c)
Precisely when .

In this case, you have so the minimum turning point occurs when:

either (invalid, reject, an exponential is never 0)

or . Now re-arrange this equation into what they want you to show.
3. (Original post by Zacken)
Precisely when .

In this case, you have so the minimum turning point occurs when:

either (invalid, reject, an exponential is never 0)

or . Now re-arrange this equation into what they want you to show.
Oh, I see!! Thank you!!
Oh, I see!! Thank you!!
No worries, can you take it from here, then?
5. (Original post by Zacken)
No worries, can you take it from here, then?
Well I've tried to use the factor theorem to factorise it but can't find any value that would make the equation equal to zero?
Well I've tried to use the factor theorem to factorise it but can't find any value that would make the equation equal to zero?
There's no easy solution. You have and you want to show that .

The obvious thing to do first, is to move the 3 to the other side to get . Then divide everything by 2 to get . This is start to look good!

Let's factorise an out of the LHS: .

Now, can you think about what to do to get:

?
7. (Original post by Zacken)
There's no easy solution. You have and you want to show that .

The obvious thing to do first, is to move the 3 to the other side to get . Then divide everything by 2 to get . This is start to look good!

Let's factorise an out of the LHS: .

Now, can you think about what to do to get:

?
No, I mean if we factorise x^2+3x+2 =(x+2)(x+1) but how do you get (2x^2+1)(x^2+1)?
No, I mean if we factorise x^2+3x+2 =(x+2)(x+1) but how do you get (2x^2+1)(x^2+1)?
You're going about this the wrong way. We don't want to solve for , we want to get an iterative formula for in terms of .

So, from:

9. (Original post by Zacken)
You're going about this the wrong way. We don't want to solve for , we want to get an iterative formula for in terms of .

So, from:

Oh, I see!! Thaank you!!
Oh, I see!! Thaank you!!
No worries. This was a bit of an odd question, to be honest.

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