(a)(i)
Let
(a)(ii)
*Students are expected to prove that gives the maximum area.
(b)(i)
latex x
latex \Rightarrow \frac{dy}{dx}=0latex y=-x^2
latex y=-x^2
latex x^3 + 2y^3 +3xy=klatex x^3 + 2(-x^2)^3 +3x(-x^2)=klatex 2x^6 + 2x^3 + k=0
latex y=-1
latex -1=-x^2latex x =\pm x
latex x = 1, k=-4
latex x = -1, k=0$