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# 3_ [Total 15 marks] Consider the functionf(,y) = 2 = e fv(a) [3 marks] Find the location in the (â‚¬,y_ plane of the critical point(s) of f (x,y), and give the ...

## Question

###### 3_ [Total 15 marks] Consider the functionf(,y) = 2 = e fv(a) [3 marks] Find the location in the (â‚¬,y_ plane of the critical point(s) of f (x,y), and give the corresponding value(s) of z. (Only consider points with finite values the coordinates, i.e. don't consider the behaviour of f at infinity). (b) [2 marks] Write down the equation of the tangent plane(s) to f (â‚¬,y) at the critical point(s) identified in part (a) , giving a brief justification of your answer: (c) [5 marks] Using the m

3_ [Total 15 marks] Consider the function f(,y) = 2 = e fv (a) [3 marks] Find the location in the (â‚¬,y_ plane of the critical point(s) of f (x,y), and give the corresponding value(s) of z. (Only consider points with finite values the coordinates, i.e. don't consider the behaviour of f at infinity). (b) [2 marks] Write down the equation of the tangent plane(s) to f (â‚¬,y) at the critical point(s) identified in part (a) , giving a brief justification of your answer: (c) [5 marks] Using the method of Lagrange multipliers, show that the extremum of f(x,y) subject to the constraint T + 2y = 4 occurs at the point (2, 1). (Again, only consider points with finite values the coordinates). (d) [5 marks] Evaluate the Taylor series expansion of f (â‚¬, y) about the point (2,1), keeping terms up to and including second partial derivatives of f _

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