(a)(i)

Let

(a)(ii)

*Students are expected to prove that gives the maximum area.

(b)(i)

latex xlatex \Rightarrow \frac{dy}{dx}=0latex y=-x^2latex y=-x^2latex x^3 + 2y^3 +3xy=klatex x^3 + 2(-x^2)^3 +3x(-x^2)=klatex 2x^6 + 2x^3 + k=0latex y=-1latex -1=-x^2latex x =\pm xlatex x = 1, k=-4latex x = -1, k=0$