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# 3. Answer all parts (a) to (f) of this question. Consider a function (z,y)

Question: 3. Answer all parts (a) to (f) of this question. Consider a function (z,y) = 10-2²-y² azy be ², where z R, y € Rand (a, b) are parameters. (a) [5 marks] Show that the derivative of eis 2.re (b) [10 marks] Write down the first-order conditions for the problem of maximising (x, y). Show that r=0; y=0 is a solution to the first-order conditions. (e) [10 marks]See the answerSee the answerSee the answer done loadingShow transcribed image textTranscribed image text: 3. Answer all parts (a) to (f) of this question. Consider a function (z,y) = 10-2²-y² azy be ², where z R, y € Rand (a, b) are parameters. (a) [5 marks] Show that the derivative of eis 2.re (b) [10 marks] Write down the first-order conditions for the problem of maximising (x, y). Show that r=0; y=0 is a solution to the first-order conditions. (e) [10 marks] Find the Hessian matrix of (x, y) at any point (x, y). (d) [10 marks] Find the condition about (a, b) under which the second-order condition for (x=0; y=0) to a be local maximum. (e) [5 marks] Show that if b>0, then (a=0; y = 0) is not a global maximum. (f) [10 marks] Show that if b < 0 and a = -1, then (r=0; y = 0) is a global maximum.

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