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...

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Extracted 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.