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implicit differentiation. watch

1. the question im stuck on is: a) show that there are turning points at (4,8) and (-4,-8) on the graph of xy+48=(x^2)+(y^2)
I think i did this bit correctly because i got that dy/dx is (y-2x)/(2y-x), which when both of the above coordinates are subbed in gives zero.
the bit i'm stuck on is: b) find the second derivative and use it to show which is a maxima and which is a minima. I had a go at it and got it wrong so can someone please explain the correct way to do this? I would type the method I used out but theres not much point because i didn't even have any idea on how to do it so i was just kind of guessing. thanks
2. Do you know what dy/dx would be if y=U/V where both V and U are functions of x and y?

Do you know how to recognise if a stationery point is a maximum or minimum by calculating the value of the second order derivative at this point, whether it is positive or negative?
3. (Original post by Gibus_pyro)
the question im stuck on is: a) show that there are turning points at (4,8) and (-4,-8) on the graph of xy+48=(x^2)+(y^2)
I think i did this bit correctly because i got that dy/dx is (y-2x)/(2y-x), which when both of the above coordinates are subbed in gives zero.
the bit i'm stuck on is: b) find the second derivative and use it to show which is a maxima and which is a minima. I had a go at it and got it wrong so can someone please explain the correct way to do this? I would type the method I used out but theres not much point because i didn't even have any idea on how to do it so i was just kind of guessing. thanks
Your result for dy/dx is correct. Now differentiate it again using the quotient rule., Then, when testing whether the second derivative is positive or negative, remember that the first derivative is zero.
4. (Original post by Gibus_pyro)
the question im stuck on is: a) show that there are turning points at (4,8) and (-4,-8) on the graph of xy+48=(x^2)+(y^2)
I think i did this bit correctly because i got that dy/dx is (y-2x)/(2y-x), which when both of the above coordinates are subbed in gives zero.
the bit i'm stuck on is: b) find the second derivative and use it to show which is a maxima and which is a minima. I had a go at it and got it wrong so can someone please explain the correct way to do this? I would type the method I used out but theres not much point because i didn't even have any idea on how to do it so i was just kind of guessing. thanks
I would have left the function as xy' + y = 2x + 2yy'

As this is easier to differentiate again rather than having to use the quotient rule with implicit differentiation
5. ahh yes quotient rule. should have seen that. thanks very much

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