QUESTION 1a

Let \(4x^2+3xy^2+7x+3y=0\).

(i) Use implicit differentiation to show that

\(\displaystyle {dy\over dx}=-{8x+3y^2+7\over 3(1+2xy)}\)

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(ii) Show that for \(f(x,y)=4x^2+3xy^2+7x+3y\),

\(\displaystyle 6 {∂f(x,y)\over ∂y}-10=\left({∂^2 f(x,y) \over ∂y^2} \right) \left({∂^2 f(x,y) \over ∂y∂x}\right)+{∂^2 f(x,y) \over ∂x^2}\)

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Discussion

C.A.P.E - PURE MATHEMATICS II EXAM SOLUTIONS