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C4 implict differentiation question

1486678318676-2132571362.jpg hi , for this question I am stuck on the y values I obtained. From my working , there are two y values worked out for each solution of x. But the mark scheme only has on y value for each x value.
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Thanks
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1486678491388738926511.jpg274.9KB
Original post by coconut64
1486678318676-2132571362.jpg hi , for this question I am stuck on the y values I obtained. From my working , there are two y values worked out for each solution of x. But the mark scheme only has on y value for each x value.
Attachment not found


Thanks
Attachment not found


Mark scheme attachment doesn't seem to be working, but you're supposed to substitute x = 2, -2 (assuming this is correct) back into the y = -x equation, not into the original curve equation.
(edited 7 years ago)
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coconut64
OP
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Original post by tajtsracc
Mark scheme attachment doesn't seem to be working, but you're supposed to substitute x = 2, -2 (assuming this is correct) back into the y = -x equation, not into the original curve equation.


why is that?
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Notnek
21
Original post by coconut64
why is that?

When dydx=0\frac{dy}{dx}=0, you have found that y=−xy=-x so you need to find where y=−xy=-x on the curve. To do that you need to solve these simultaneous equations:

y=−xy=-x
x2+2xy−3y2+16=0x^2+2xy-3y^2+16=0

You solved these equations to get x=2x=2 and x=−2x=-2. If you remember (GCSE) you can normally plug in these into either of your simultaneous equations to get the yy values. So it's best to choose the simpler one y=−xy=-x. You can use the more complicated equation but that will give you two yy solutions and only one of them will also be valid in y=−xy=-x so you'd have to check.

So it makes sense to always plug the xx values into the simpler equation. Does this make sense?

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