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For the following functions f and g : f(x, y) = e ax ? (1 ?...

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Advance Math

For the following functions f and g

: f(x, y) = e ax ? (1 ? a)lny a > 0 g(x, y, z) = ?3x 2 ? 3y 2? 3z 2 + 2xy + 2xz + 2yz

1.

Calculate the Hessian matrices of f and g noted Hf (x, y) andHg(x, y, z)

2. Show that Hg(x, y, z) is define negativly for all (x, y, z) ?Dg

3. For what value o a is , Hf (x, y) define positivly for any(x, y) ? Df ?

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