Define if x <0 f(x) : 1 { 2x if x > 0 Show that f(x) is continuous on I = [-1, 2] (which means that Extreme Value Theorem applies). Show that (0, 1) is a critical point of f(x). Determine the absolute extrema of f on I = [-1,2].

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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Define
S 2"
f(x) =
| 1– 2x
if x < 0
if x > 0
Show that f(x) is continuous on I = [–1,2] (which means that Extreme Value Theorem
аpplies).
Show that (0, 1) is a critical point of f(x).
Determine the absolute extrema of f on I = [-1,2|.
Transcribed Image Text:Define S 2" f(x) = | 1– 2x if x < 0 if x > 0 Show that f(x) is continuous on I = [–1,2] (which means that Extreme Value Theorem аpplies). Show that (0, 1) is a critical point of f(x). Determine the absolute extrema of f on I = [-1,2|.
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