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C3 Differentiation Question

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.

Thanks in advance :smile:

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Reply 1

JLegion

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 :smile:

(edited 7 years ago)

Reply 2

TSR George

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 :smile:

Sure, here you go :smile:

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

Reply 3

JLegion

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 :smile:

Reply 4

RDKGames

Study Forum Helper

Original post by Lollieboo

SOLUTION

Please do not post full solutions on this forum as it's against the rules.

Reply 5

BlueSpikes

Original post by RDKGames

Please do not post full solutions on this forum as it's against the rules.

Is it? Why is that :frown:

they are really useful.

Reply 6

RDKGames

Study Forum Helper

Full working for a part of the question, they clearly did half the question for you rather than point you in the right direction.

Reply 7

RDKGames

Study Forum Helper

Original post by bobwibbles

Is it? Why is that :frown:

they are really useful.

Read here: http://www.thestudentroom.co.uk/showthread.php?t=4066671&p=64637319#post64637319

Reply 8

Lollieboo

Original post by RDKGames

Read here: http://www.thestudentroom.co.uk/showthread.php?t=4066671&p=64637319#post64637319

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.

Reply 9

RDKGames

Study Forum Helper

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.

Reply 10

JLegion

rayquaza17

How to Answer Questions
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.

Reply 11

Lollieboo

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.