2. Show that the following functions are convex by verifying the condition that V² f(x) 20 is satisfied for all a in the domain of f: (a) f(un, u₂) In(e" + e"), (b) f(u, uz, us, UA) -In(1-₁-2-3-4) over the domain {u E R¹|u₁+uz+us+u₁ < 1}.

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Q: 2. Show that the following functions are convex by verifying the condition that V²f(x) 20 is…

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A: We have,

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A: As per guidelines, I can do only first three subparts of the question.

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Q: 5. Determine the vclue of c such that the function is continuous on (-o0,00 + flx) = 2x, x SC

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A: Given that

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A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

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Q: Let f be a differentiable real function defined in (a, b). Prove that f is convex if and only if f'…

A: A function f is convex in a domain a,b if for all 0≤λ≤1, fλx1+(1-λ)x2≤λfx1+1-λfx2  ∀x1,x2∈a,b. Also…