7. Consider the function f(x) defined on the set by D = {x = R3: x > 0, Xz > 0, Xg >0} = f(x) = (x₁)¹ + (x₂)²² + (x3)²³, where ri> 0 for i 1, 2, 3. = 1, 2, 3. (a) Show that f(x) is strictly convex on D if r; > 1 for i (b) Show that f(x) is strictly concave on D if 0 < r; < 1 for i = 1, 2, 3.

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A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

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Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: 2. Show that the following functions are convex by verifying the condition that V² f(x) 20 is…

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Q: (#4) When is a function f(.): R" R convex and proper? Show that f(-) is convex and proper implies…

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Q: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

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Q: a)Suppose f: R → Z, where f(x) = [x + ¹] i. Graph the function f(x). ii. If A = {x: 1 ≤ x ≤ 3}, find…

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Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

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