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attached is a word document including my question an answer as I wanted to include diagrams. the question is a M2 question

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What is the point of a derivative?


The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.


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