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

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) and Hg(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 ?

Expert Solution

Colby Messinger answered 2 years ago

For the following functions f and g : f(x, y) = e^ax − (1 − a)lny...

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) and Hg(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...

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