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2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.

2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 64E
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2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.
Transcribed Image Text:2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.
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