# implicit differentiation.Watch

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#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
0
5 years ago
#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?
0
5 years ago
#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.
0
5 years ago
#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
0
#5
ahh yes quotient rule. should have seen that. thanks very much
0
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