Question 1: a. Check if the following functions are: Convex? Concave? Strictly Convex? Strictly Concave? fix) = 2x,-3 x,x; – 1/4 x3 – 5 x2 • (x) = (x)- 2x2) + (x; – 2x3)° + (X3 – 4)° b. Determine the Hessian matrix of the following function: f(Xi, X2, X3) (2x- 3x2) +4 x

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 1:
a. Check if the following functions are:
Convex?
Concave?
Strictly Convex?
Strictly Concave?
•(x) = 2x,-3 x,x3-1/4 x;-5 x2
%D
f(x) = (x-2x) + (x2- 2x3) + (x3- 4)°
b. Determine the Hessian matrix of the following function:
f(X, X2, X3) (2x - 3x2) + 4 x;
3x2)+4 x
Transcribed Image Text:Question 1: a. Check if the following functions are: Convex? Concave? Strictly Convex? Strictly Concave? •(x) = 2x,-3 x,x3-1/4 x;-5 x2 %D f(x) = (x-2x) + (x2- 2x3) + (x3- 4)° b. Determine the Hessian matrix of the following function: f(X, X2, X3) (2x - 3x2) + 4 x; 3x2)+4 x
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