3. Let f : (-0, 2) → R be the function given by 5 +1 0

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.2: Linear Functions And Applications
Problem 33PS
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3. Let f : (-0,2) →R be the function given by
2 +z 0<I< 2
f(x) = {33 -
arctan(r)
r<0.
a) Explain whyf is differentiable at a = 0 and give the value of f'(0).
b) What is value of the infimum of f and what is value of the supremum of f? Does f have
a maximum or a minimum? If so, then state the values of a at which the maximum or
minimum occur.
c) Explain why r 0 is an inflection point of f.
Transcribed Image Text:3. Let f : (-0,2) →R be the function given by 2 +z 0<I< 2 f(x) = {33 - arctan(r) r<0. a) Explain whyf is differentiable at a = 0 and give the value of f'(0). b) What is value of the infimum of f and what is value of the supremum of f? Does f have a maximum or a minimum? If so, then state the values of a at which the maximum or minimum occur. c) Explain why r 0 is an inflection point of f.
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