FRE6083_HW3

# FRE6083_HW3 - FRE 6083 Homework 3 Question 1 Dierentiation...

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FRE 6083 Homework 3 Question 1 Differentiation practice. Find the first derivative of the function 10 0 . 5 u1D465 2 + uni221A.alt01 log(1 + u1D465 2 ) + 4 log( u1D465 ) exp( u1D465 ) Question 2 Partial derivatives of a multivariable function. The stationary points of a function of several variables are found by setting all the partial derivatives to zero and solving the resulting set of equations—the first order conditions . The second order conditions , properties of the Hessian, determine the type of stationary point—minimum, maximum, saddle point,... (a) Calculate the gradient vector of the function u1D453 ( u1D465, u1D466 ) = u1D465 2 u1D466 2 u1D465 4 u1D466 and hence find the stationary points, if any. (b) Calculate the Hessian of the function in (a). Compute the eigenvalues of the Hessian at the stationary points found in (a). In each case determine if the Hessian is positive definite or negative definite. Question 3 Simplifying determinants.

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