Explain how f(x) = |x| is an example of a function that is continuous everywhere, but its derivative is not continuous, and Give an example of a function that is continuous everywhere, and whose derivative is continuous everywhere, but whose second derivative is not continuous. Justify your solution.
Explain how f(x) = |x| is an example of a function that is continuous everywhere, but its derivative is not continuous, and Give an example of a function that is continuous everywhere, and whose derivative is continuous everywhere, but whose second derivative is not continuous. Justify your solution.
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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Transcribed Image Text:Explain how
f(x) = |x|
is an example of a function that is continuous everywhere, but its derivative is not continuous, and Give an example of a
function that is continuous everywhere, and whose derivative is continuous everywhere, but whose second derivative is
not continuous. Justify your solution.
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