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[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

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thecandydoll:
The equation of a curve is x3 + 2y3 = 3xy.
 Find the coordinates of the point, other than the origin, where the curve has a tangent which is
parallel to the x-axis.   [5]

elemis:

--- Quote from: thecandydoll on May 13, 2011, 07:30:45 am ---The equation of a curve is x3 + 2y3 = 3xy.
 Find the coordinates of the point, other than the origin, where the curve has a tangent which is
parallel to the x-axis.   [5]

--- End quote ---

Use implicit differentiation and equate to zero. Solve.

thecandydoll:

The equation of a curve is xy(x + y) = 2a3, where a is a non-zero constant. Show that there is only one point on the curve at which the tangent is parallel to the x-axis, and find the coordinates of this point.

I dont get how to do this/

thecandydoll:
May june 2008
Q8 I don't get this either.
Someshow me the workingg?

elemis:

--- Quote from: thecandydoll on May 14, 2011, 07:04:31 am ---The equation of a curve is xy(x + y) = 2a3, where a is a non-zero constant. Show that there is only one point on the curve at which the tangent is parallel to the x-axis, and find the coordinates of this point.

I dont get how to do this/

--- End quote ---

You are told ' a'  is a non-zero constant. So, if you want, you can think of 2a3 as some number. When you differentiate a number like 10, for example, you simply get zero.

Hence :

x2y + xy2 = 2a3

Use the product rule for the left hand side terms and simply differentiate 2a3 to get zero because, after all, its nothing but a number.

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