Problems 1. Consider the function f: R R given by where a, b, xER. (a) Find...

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Problems 1. Consider the function f: R" R given by where a, b, xER". (a) Find Vf(x) and V2f(x). (b) Verify your result for x f(x) = (xa)(bx), x = R, a = [1, -1], b = [2,3]T. (c) In (b) check whether V2f(x) is positive or negative definite. (d) What is the rank of Vf(x) for different values of x E R? Problems 1. Consider the function f: R" R given by where a, b, xER". (a) Find Vf(x) and V2f(x). (b) Verify your result for x f(x) = (xa)(bx), x = R, a = [1, -1], b = [2,3]T. (c) In (b) check whether V2f(x) is positive or negative definite. (d) What is the rank of Vf(x) for different values of x E R?