Question 5 (50% - Modified Version of a Past Exam Question) Let (x) = f(x, x2)...

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Question 5 (50% - Modified Version of a Past Exam Question) Let (x) = f(x, x2) = (2x + 3x2) + (x2 1), where x = [x1, x2] R. (a) Find the gradient vector Vf(x) and the Hessian matrix V(x) of (x). (b) Determine the condition(s) for x under which f(x) is strictly convex. (c) Using Taylor's Theorem, approximate f(x) by a quadratic function q(x) at the point [1, 2]T. (d) Approximate f(1.7, 1.7) by the quadratic function q(x) about the point [1,2]. How many significant figures do that particular quadratic approximation have? (e) Show that V2(1, 1) is positive semi-definite by principal minor test. Question 5 (50% - Modified Version of a Past Exam Question) Let (x) = f(x, x2) = (2x + 3x2) + (x2 1), where x = [x1, x2] R. (a) Find the gradient vector Vf(x) and the Hessian matrix V(x) of (x). (b) Determine the condition(s) for x under which f(x) is strictly convex. (c) Using Taylor's Theorem, approximate f(x) by a quadratic function q(x) at the point [1, 2]T. (d) Approximate f(1.7, 1.7) by the quadratic function q(x) about the point [1,2]. How many significant figures do that particular quadratic approximation have? (e) Show that V2(1, 1) is positive semi-definite by principal minor test.

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ANSWER a To find the gradient vector fx and the Hessian matrix fx of fx Gradient vector fx The gradient vector is a vector of the first partial derivatives of the function fx fx 2x1 3x2 x2 1 The parti... View the full answer