Consider the function f: R2 R, given by f(x1, x2) where t is a free...

   

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Consider the function f: R2 → R, given by f(x1, x2) where t is a free parameter (a number). = -x²+2x² + 4x1x2 + 4x²2. (a) For any value of the parameter t, identify all critical points of the function f. Precisely motivate your answer. [6 marks] (b) Specify how the number of critical points depends on the value of the param- eter t. Precisely motivate your answer. [3 marks] (c) For any value of the parameter t, characterise each of the critical points of the function f as a local maximum, minimum, or a saddle point. Precisely motivate your answer. [6 marks] (d) For every value of the parameter t, determine whether the function f has a global maximum or a global minimum. Precisely motivate your answer. marks] Consider the function f: R2 → R, given by f(x1, x2) where t is a free parameter (a number). = -x²+2x² + 4x1x2 + 4x²2. (a) For any value of the parameter t, identify all critical points of the function f. Precisely motivate your answer. [6 marks] (b) Specify how the number of critical points depends on the value of the param- eter t. Precisely motivate your answer. [3 marks] (c) For any value of the parameter t, characterise each of the critical points of the function f as a local maximum, minimum, or a saddle point. Precisely motivate your answer. [6 marks] (d) For every value of the parameter t, determine whether the function f has a global maximum or a global minimum. Precisely motivate your answer. marks]

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To find the critical points of the function f we need to find the values of x1 and x2 ... View the full answer