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You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second...

You are given that the function f(x,y)=8x2+y2+2x2y+3 has first partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the point (0,0). Which one of the following statements is true?

  • A. (0,0) is not a critical point of f(x,y).

  • B. f(x,y) has a saddle point at (0,0).

  • C. f(x,y) has a local maximum at (0,0).

  • D. f(x,y) has a local minimum at (0,0).

  • E. The second derivative test provides no information about the behaviour of f(x,y) at the point (0,0).

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