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Let f(x) = 1 and 1 if x > 0 g(x) 8 +- if x < 0 Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f-g is constant?

Let f(x) = 1 and 1 if x > 0 g(x) 8 +- if x < 0 Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f-g is constant?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?
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== and Let f(x) if x > 0 g(x) 1 8 + if x < 0 Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f -g is constant? If f'(x) = g'(x) for all x in an interval (a, b), then f- g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant. For x > 0, f(x) = g(x), so f'(x) = g'(x). For x < 0, f'(x) = and g'(x) = so f'(x) ? g'(x). However, the domain of g(x) is not an interval [it is (-o, 0) U (0, 0)] so we cannot conclude that f- g is constant (in fact it is not). Need Help? Read It Watch It
Transcribed Image Text:== and Let f(x) if x > 0 g(x) 1 8 + if x < 0 Show that f'(x) = g'(x) for all x in their domains. Can we conclude from the corollary below that f -g is constant? If f'(x) = g'(x) for all x in an interval (a, b), then f- g is constant on (a, b); that is, f(x) = g(x) + c where c is a constant. For x > 0, f(x) = g(x), so f'(x) = g'(x). For x < 0, f'(x) = and g'(x) = so f'(x) ? g'(x). However, the domain of g(x) is not an interval [it is (-o, 0) U (0, 0)] so we cannot conclude that f- g is constant (in fact it is not). Need Help? Read It Watch It
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