QA: (inspired by a problem from Stewart's textbook) Suppose that there is some function f whose _derivative_ is f'=sin(x)/x, with f (0)=1 by definition rather than DNE. Draw that, on the interval [-4pi,+4pi]. (i) On what intervals is the original f increasing? Decreasing? Indicate the intervals on the graph as well as writing them in interval notation like [0,pi] (ii) At what x values does f have a local max? A local min? Indicate them on the graph as well as writing them out like: maxes at ... ; mins at .... p....
QA: (inspired by a problem from Stewart's textbook) Suppose that there is some function f whose _derivative_ is f'=sin(x)/x, with f (0)=1 by definition rather than DNE. Draw that, on the interval [-4pi,+4pi]. (i) On what intervals is the original f increasing? Decreasing? Indicate the intervals on the graph as well as writing them in interval notation like [0,pi] (ii) At what x values does f have a local max? A local min? Indicate them on the graph as well as writing them out like: maxes at ... ; mins at .... p....
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![QA: (inspired by a problem from Stewart's textbook) Suppose that
there is some function f whose _derivative_ is f'=sin(x)/x, with f
'(0)=1 by definition rather than DNE. Draw that, on the interval
[-4pi,+4pi].
(i) On what intervals is the original f increasing? Decreasing?
Indicate the intervals on the graph as well as writing them in
interval notation like [0,pi]
(ii) At what x values does f have a local max? A local min? Indicate
them on the graph as well as writing them out like: maxes at ...;
mins at ....
(iii) On what intervals is f CD? CU? Indicate the intervals on the
graph as well as writing them in interval notation. You won't be able
to find the exact values using formulas; approximate values are
fine.
(iv) At what x values does f have an inflection point? Indicate them
on the graph as well as writing them out like: IP at
approximate values are fine, since it's impossible to find exact
values]
(v) Sketch a graph of f, starting at f(0)=0.
[again,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F498b7902-5673-468d-94e7-10f30e531304%2Fcd82c999-23b0-42e5-bfda-74d9b4815951%2Foivzzlw7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QA: (inspired by a problem from Stewart's textbook) Suppose that
there is some function f whose _derivative_ is f'=sin(x)/x, with f
'(0)=1 by definition rather than DNE. Draw that, on the interval
[-4pi,+4pi].
(i) On what intervals is the original f increasing? Decreasing?
Indicate the intervals on the graph as well as writing them in
interval notation like [0,pi]
(ii) At what x values does f have a local max? A local min? Indicate
them on the graph as well as writing them out like: maxes at ...;
mins at ....
(iii) On what intervals is f CD? CU? Indicate the intervals on the
graph as well as writing them in interval notation. You won't be able
to find the exact values using formulas; approximate values are
fine.
(iv) At what x values does f have an inflection point? Indicate them
on the graph as well as writing them out like: IP at
approximate values are fine, since it's impossible to find exact
values]
(v) Sketch a graph of f, starting at f(0)=0.
[again,
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