Consider a function π (x, y) = 10-2² - y² + axy + bez²+y², where x ∈ R, y ∈ R and (a, b) are parameters. (a) Show that the derivative of e² is 2xe*². (b) Write down the first-order conditions for the problem of maximising 7 (x, y). Show that 0; y = 0 is a solution to the first-order conditions.
(c) Find the Hessian matrix of 7 (x, y) at any point (x, y). (d) Find the condition about (a, b) under which the second-order condition for (x=0; y = 0) to a be local maximum. (e)Show that if b>0, then (z= 0; y = 0) is not a global maximum. (f) Show that if b < 0 and a = -1, then (x=0; y = 0) is a global maximum.