II. Show that if preferences are strictly convex, then A'(z®) is strictly convex for each ° € X'.
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- Find the minimum value of z =x2 + y2 subject to the condition x + y = 18.Suppose D : P(R) → P(R) is a linear map such that deg D(p) = (deg p) − 1. Show that D is surjective. Explain why for every p ∈ P(R), there exists a q ∈ P(R) such that 5q′′ +3q′ = p. Solve for q if p(x) = x^2 + x + 1.Let f(x,y,z)=(x^4)y+z^4 and x=st^2, y=st, and z=(s^2)t.