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Let f: C → R, with C = (-10, 10) c R be given as f(x) = |x| (absolute value of x). (a Sketch epi(f). (b Find two of the subgradients of ƒ at x = 0. (c Find the set of all subgradients of f at x = 1.

Let f: C → R, with C = (-10, 10) c R be given as f(x) = |x| (absolute value of x). (a Sketch epi(f). (b Find two of the subgradients of ƒ at x = 0. (c Find the set of all subgradients of f at x = 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Let \( f: C \to \mathbb{R} \), with \( C = (-10, 10) \subset \mathbb{R} \) be given as \( f(x) = |x| \) (absolute value of \( x \)). (a) Sketch \(\text{epi}(f)\). (b) Find two of the subgradients of \( f \) at \( x = 0 \). (c) Find the set of all subgradients of \( f \) at \( x = 1 \).
Transcribed Image Text:5. Let \( f: C \to \mathbb{R} \), with \( C = (-10, 10) \subset \mathbb{R} \) be given as \( f(x) = |x| \) (absolute value of \( x \)). (a) Sketch \(\text{epi}(f)\). (b) Find two of the subgradients of \( f \) at \( x = 0 \). (c) Find the set of all subgradients of \( f \) at \( x = 1 \).
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