Exercise 4:[Challenge] Letf be a function that is everywhere differentiable. Prove that f' has no jump dis- continuities or removable discontinuities. Remark: I consider this exercise important, since it shows that there exist many functions that are not the derivative of another function. We will show next quarter that every continuous function is the derivative of some function.
Exercise 4:[Challenge] Letf be a function that is everywhere differentiable. Prove that f' has no jump dis- continuities or removable discontinuities. Remark: I consider this exercise important, since it shows that there exist many functions that are not the derivative of another function. We will show next quarter that every continuous function is the derivative of some function.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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ex4 hw4
![Exercise 4:[Challenge] Letf be a function that is everywhere differentiable. Prove that f' has no jump dis-
continuities or removable discontinuities.
Remark: I consider this exercise important, since it shows that there exist many functions that are
not the derivative of another function. We will show next quarter that every continuous function is the
derivative of some function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff121ba60-7058-4a7c-893c-99f8ff2d6afa%2F5c817202-c934-494e-b576-dd0d3669b697%2Fm191m37.png&w=3840&q=75)
Transcribed Image Text:Exercise 4:[Challenge] Letf be a function that is everywhere differentiable. Prove that f' has no jump dis-
continuities or removable discontinuities.
Remark: I consider this exercise important, since it shows that there exist many functions that are
not the derivative of another function. We will show next quarter that every continuous function is the
derivative of some function.
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