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# C3 Differentiation Question

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1. Hi,

Could someone else please do this question and let me know what you get for it? I don't get the same answer as what is in the back of the book.

The question says:
Show that the curve y=(x+3)(x+4)^-2 has a single stationary point
Find the coordinates of the stationary point and determine its nature.

2. (Original post by Blake Jones)
Hi,

Could someone else please do this question and let me know what you get for it? I don't get the same answer as what is in the back of the book.

The question says:
Show that the curve y=(x+3)(x+4)^-2 has a single stationary point
Find the coordinates of the stationary point and determine its nature.

Would you mind being clearer? The equation you posted is ambiguous. Either it means:
y = (x+3) x [(x+4)^-2] or
y = [(x+3)(x+4)]^-2

Also, it would probably benefit you more if you posted your workings so we can spot any mistakes
3. (Original post by JLegion)
Would you mind being clearer? The equation you posted it ambiguous. Either it means:
y = (x+3) x [(x+4)^-2] or
y = [(x+3)(x+4)]^-2

Also, it would probably benefit you more if you posted your workings so we can spot any mistakes
Sure, here you go And I meant the first one
y = (x+3) x [(x+4)^-2]
dy/dx = -2(x+4)^-3 + (x+3)[(x+4)^-2]
dy/dx = 0
dy/dx = (x+4)^-3[(x+3)(x+4)-2)
0 = (x+2)(x+5) / (x+4)^3
x = -2 and x = -5
When x = -2 y= 1/4 so the coordinate is (-2, 1/4) The answer agrees with this part
d^2y/dx^2 = (2x+7)(x+4) -3(x+2)(x+5) / (x+4)^4
When x = -2 this = 6/16 = 3/13 which means it's a minimum point

But the answer says it's a maximum point
4. Ah I see where I've gone wrong, thank you!
5. (Original post by Blake Jones)
Sure, here you go And I meant the first one
y = (x+3) x [(x+4)^-2]
dy/dx = -2(x+4)^-3 + (x+3)[(x+4)^-2]
dy/dx = 0
dy/dx = (x+4)^-3[(x+3)(x+4)-2)
0 = (x+2)(x+5) / (x+4)^3
x = -2 and x = -5
When x = -2 y= 1/4 so the coordinate is (-2, 1/4) The answer agrees with this part
d^2y/dx^2 = (2x+7)(x+4) -3(x+2)(x+5) / (x+4)^4
When x = -2 this = 6/16 = 3/13 which means it's a minimum point

But the answer says it's a maximum point
I believe you have differentiated incorrectly.
Using the product rule, dy/dx = v(du/dx) + u(dv/dx)
Whereas, you appear to have used dy/dx = (du/dx)(dv/dx) + uv
It should be: dy/dx = -2(x+4)^(-3)(x+3) + [(x+4)^-2] instead
6. (Original post by Lollieboo)
SOLUTION
Please do not post full solutions on this forum as it's against the rules.
7. (Original post by RDKGames)
Please do not post full solutions on this forum as it's against the rules.
It's okay, it's not full, they didn't show me how to do the nature of the stationary point bit
8. (Original post by RDKGames)
Please do not post full solutions on this forum as it's against the rules.
Is it? Why is that they are really useful.
9. (Original post by Blake Jones)
It's okay, it's not full, they didn't show me how to do the nature of the stationary point bit
Full working for a part of the question, they clearly did half the question for you rather than point you in the right direction.
10. (Original post by bobwibbles)
Is it? Why is that they are really useful.
11. It's not against the rules, it only advises not to necessarily post full solutions, as it's better to let people think on their own.
12. (Original post by Lollieboo)
It's not against the rules, it only advises not to necessarily post full solutions, as it's better to let people think on their own.
I think you missed the big bold bit which says "Do not post full solutions" within that post which strictly forbids full solutions.
13. (Original post by rayquaza17)
The aim here is to show the original poster how they can answer the question. There is actually quite a lot of skill and experience involved in doing this well. For example, if they are stuck using a particular method, the ideal is to show them how to get that method to work, not to show them a solution using a completely different technique.

In general, the best approach is to give small 'nudges' in the right direction. Do not post full solutions.
See above.
14. (Original post by RDKGames)
I think you missed the big bold bit which says "Do not post full solutions" within that post which strictly forbids full solutions.
Alright calm down cowboy. If you go to the 'report a post section', there is no option to report someone for giving a full solution or similar. So personally I only guidance of how to answer questions. No rules or strictly forbidding anything.
15. (Original post by Lollieboo)
Alright calm down cowboy. If you go to the 'report a post section', there is no option to report someone for giving a full solution or similar. So personally I only guidance of how to answer questions. No rules or strictly forbidding anything.
Yes there is. Not constructive.
16. I still can't get it to be a minimum point though, for the 2nd differential I got

(x+4)^-4 [(x+4)-3(x+2)]

is this right?
17. (Original post by Blake Jones)
I still can't get it to be a minimum point though, for the 2nd differential I got

(x+4)^-4 [(x+4)-3(x+2)]

is this right?
Looks like you're a factor of -1 off. Check your minus signs.
18. (Original post by Blake Jones)
I still can't get it to be a minimum point though, for the 2nd differential I got

(x+4)^-4 [(x+4)-3(x+2)]

is this right?
19. (Original post by Zacken)
Looks like you're a factor of -1 off. Check your minus signs.
Ah I see! so it's a maximum because the second differential= -1/8
20. (Original post by Blake Jones)
Ah I see! so it's a maximum because the second differential= -1/8
Yep, if the second derivative is less than 0 (i.e negative) then it's a maximum. Have you spotted why you got It should be - you probably forgot a minus whilst differentiating or something.

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