Question: [ M a x i m u m mark: 8 ] Consider the curve with equation x 3 + y 3 = 4 x y

[Maximum mark: 8]
Consider the curve with equation x3+y3=4xy.
(a) Use implicit differentiation to show that dy(d)x=4y-3x23y2-4x.
The tangent to this curve is parallel to the x-axis at the point where x=k,k>0.
(b) Find the value ofk.
[ M a x i m u m mark: 8 ] Consider the curve with

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