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C4 Implicit Differentiation Help!

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IO4567:
Please could anyone help me here - I'm blank.

x2 + 2xy - 3y2 + 16 = 0

Find the coordinates of the points on the curve where dy/dx = 0.

I've done the differentiation correctly (I think) and got this:

-2x -2y
______   = 0

2x - 6y


But now I have no idea what to do to get the coordinates! Someone please help!
In the markscheme it says 'Eliminating either variable and solving for at least one value of x or y'.

How do I 'eliminate either variable'?

Thank you so much!

~ A.F ~:

--- Quote from: IO4567 on April 27, 2010, 06:40:19 pm ---Please could anyone help me here - I'm blank.

x2 + 2xy - 3y2 + 16 = 0

Find the coordinates of the points on the curve where dy/dx = 0.

I've done the differentiation correctly (I think) and got this:

-2x -2y
______   = 0

2x - 6y


But now I have no idea what to do to get the coordinates! Someone please help!
In the markscheme it says 'Eliminating either variable and solving for at least one value of x or y'.

How do I 'eliminate either variable'?

Thank you so much!

--- End quote ---

Yuo  u got the diff right..

now.u equte the numerator to zero..as its not possible to have a zero denominator:

-2x-2y=0

2x=-2y

x=-y

then substitute x in the original equation with -y...try it and tell me :)

7ooD:
ok look dude when dy/dx=0 this means ur differentiation should be 0 i have done my differentiation as (2x+2y)/(-2x+6y)  now throw the denominator away cuz u cnt divide anything by 0 and then take the nominator =0 as for the differentiantion to be 0 nomintor should be 0

soz 2x+2y=0 get the x to 0 or y to 0 and substitute in the equation final answer should be  (0,sq root 16/3) (0,-sq root 16/3)

IO4567:
wow! thank you guys so much! really appreciate the help! cheers

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