Suppose f is differentiable at a and f(a) # 0.(a) Prove |f| is differentiable at a by using that |f| = Vf2. What are the possible values of |fl'(a)?(b) Give a counterexample that shows the conclusion need not hold if f(a) = 0. Identify where yourcalculations for (a) fail in this case.

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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.

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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Suppose f is differentiable at a and f(a) # 0.
(a) Prove |f| is differentiable at a by using that |f| = Vf2. What are the possible values of |fl'(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.

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I don't understand this step. I think if should be |f(x)-f(a)|<e when |x-a|<d.

f(x) - f(a)
x-a
whenever
1x-a) < S
- M) < ein
<E,

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