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Differentiation; Curves, Stationary Points and Table - HSN forum

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Differentiation; Curves, Stationary Points and Table


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#1 Jones

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Posted 26 August 2008 - 07:00 PM

Towards the end of the differentiation topic, I got increasingly confused! blink.gif

I understand about stationary points, but i dont understand what the table to find the maximum or minimum turning points unsure.gif

Could someone explain the purpose of the table (see attached file) , please! rolleyes.gif

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#2 Marcus

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Posted 26 August 2008 - 07:08 PM

QUOTE(Jones @ Aug 26 2008, 08:00 PM) View Post
Towards the end of the differentiation topic, I got increasingly confused! blink.gif

I understand about stationary points, but i dont understand what the table to find the maximum or minimum turning points unsure.gif

Could someone explain the purpose of the table (see attached file) , please! rolleyes.gif


What exactly is confusing you? What the table tells you, or how to work out the table?

if it is the point of the table....well it is simply to tell us if the stationary point is a maximum, minimum or point of inflexion, otherwise you would have to draw out the graph to find that out biggrin.gif
=-=-=Marcus=-=-=

#3 Jones

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Posted 26 August 2008 - 08:03 PM

QUOTE(Marcus @ Aug 26 2008, 08:08 PM) View Post
QUOTE(Jones @ Aug 26 2008, 08:00 PM) View Post
Towards the end of the differentiation topic, I got increasingly confused! blink.gif

I understand about stationary points, but i dont understand what the table to find the maximum or minimum turning points unsure.gif

Could someone explain the purpose of the table (see attached file) , please! rolleyes.gif


What exactly is confusing you? What the table tells you, or how to work out the table?

if it is the point of the table....well it is simply to tell us if the stationary point is a maximum, minimum or point of inflexion, otherwise you would have to draw out the graph to find that out biggrin.gif



I think i know what the table tells you, as I understand that a negative slope has a negative derived function, i just need to know how the table works, and how you end up with the positive and negative answers/slopes laugh.gif blink.gif

#4 Azie

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Posted 28 August 2008 - 11:32 PM

ok, id probably b better explaining this in person with a pen an paper than on here but here goes ...if u look at ur table, the rows (x, f'(x) an slope) will always b the same in every table like that ...now, 2 use the table u need a stationary point, sumtimes u have 2 work it out for urself but thats a different matter, but if u look at the question, it tells u that the stationary points r (1,5) and (2,4), so using (2,4) in this example, u no ur x row an can fill it in with 2-, 2, an 2+ (the - and + will always b like that, only the number changes) ...now, in the question it doesnt give u an f(x) equation which ull need 2 differentiate 2 get ur f'(x), but for explanation sakes, lets take f(x) = 3x^2 - 12x, wen u differentiate this, u get f'(x) = 6x - 12 ...now this is wen u use ur x row, its always easier 2 start with the middle number which here is 2, so all u have 2 do is substitute the number 2 where ever u see an x, so it becums f'(x) = 6(2) - 12 = 12 - 12 = 0 which is wat ur table gives u ...now it can get a bit harder with the other 2 numbers, take then 2-, this means that u have 2 choose a number smaller than 2 but never really go for 0 so ur best option wud b 2 use 1, so it becums f'(x) = 6(1) - 12 = 6 - 12 = -6 which is wat ur tables gives u ...do the same for the 2+ by using 3 so u get f'(x) = 6(3) - 12 = 18 -12 = +6 which is wat ur table also gives u ...thats all u have 2 do really, get a stationary point, differentinate ur equation, sub ur x point in 2 the f'(x) an record ur answers ...sorry 2 go on lol, hope it helps tho smile.gif

#5 Jones

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Posted 01 September 2008 - 07:43 PM

QUOTE(Azie @ Aug 29 2008, 12:32 AM) View Post
ok, id probably b better explaining this in person with a pen an paper than on here but here goes ...if u look at ur table, the rows (x, f'(x) an slope) will always b the same in every table like that ...now, 2 use the table u need a stationary point, sumtimes u have 2 work it out for urself but thats a different matter, but if u look at the question, it tells u that the stationary points r (1,5) and (2,4), so using (2,4) in this example, u no ur x row an can fill it in with 2-, 2, an 2+ (the - and + will always b like that, only the number changes) ...now, in the question it doesnt give u an f(x) equation which ull need 2 differentiate 2 get ur f'(x), but for explanation sakes, lets take f(x) = 3x^2 - 12x, wen u differentiate this, u get f'(x) = 6x - 12 ...now this is wen u use ur x row, its always easier 2 start with the middle number which here is 2, so all u have 2 do is substitute the number 2 where ever u see an x, so it becums f'(x) = 6(2) - 12 = 12 - 12 = 0 which is wat ur table gives u ...now it can get a bit harder with the other 2 numbers, take then 2-, this means that u have 2 choose a number smaller than 2 but never really go for 0 so ur best option wud b 2 use 1, so it becums f'(x) = 6(1) - 12 = 6 - 12 = -6 which is wat ur tables gives u ...do the same for the 2+ by using 3 so u get f'(x) = 6(3) - 12 = 18 -12 = +6 which is wat ur table also gives u ...thats all u have 2 do really, get a stationary point, differentinate ur equation, sub ur x point in 2 the f'(x) an record ur answers ...sorry 2 go on lol, hope it helps tho smile.gif



Thank you so much!!! I have a maths NAB in a week and needed to know this. rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif rolleyes.gif





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