Suppose f is differentiable at a and f(a) + 0. (a) Prove |f| is differentiable at a by using that |f| = /f². What are the possible values of |f|'(a)? (b) Give a counterexample that shows the conclusion need not hold if f(a) = 0. Identify where your calculations for (a) fail in this case.
Suppose f is differentiable at a and f(a) + 0. (a) Prove |f| is differentiable at a by using that |f| = /f². What are the possible values of |f|'(a)? (b) Give a counterexample that shows the conclusion need not hold if f(a) = 0. Identify where your calculations for (a) fail in this case.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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I don't understand this step. I think if should be |f(x)-f(a)|<e when |x-a|<d.
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