a) Determine its domain, and vertical and horizontal asymptotes (if any) b) Find the coordinates (both coordinates) of its critical points, the intervals where the function is increasing/decreasing, and classify each critical point as a local max or min c) Find the intervals where the function is concave up/concave down, and determine the coordinates (both coordinates) of the inflections points d) Determine the y-intercept (if any) e) Use this information to sketch the graph of the function. Your graph should clearly show all of the information found above

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 96E
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The function f(x) = ln x / x has a derivative f’(x) = 1-ln x/x^2 and f”(x)= 2 ln x-3/x^3
a) Determine its domain, and vertical and horizontal asymptotes (if any)
b) Find the coordinates (both coordinates) of its critical points, the intervals where the function is increasing/decreasing,
and classify each critical point as a local max or min
c) Find the intervals where the function is concave up/concave down, and determine the coordinates (both coordinates) of
the inflections points
d) Determine the y-intercept (if any)
e) Use this information to sketch the graph of the function. Your graph should clearly show all of the information found
above
Transcribed Image Text:a) Determine its domain, and vertical and horizontal asymptotes (if any) b) Find the coordinates (both coordinates) of its critical points, the intervals where the function is increasing/decreasing, and classify each critical point as a local max or min c) Find the intervals where the function is concave up/concave down, and determine the coordinates (both coordinates) of the inflections points d) Determine the y-intercept (if any) e) Use this information to sketch the graph of the function. Your graph should clearly show all of the information found above
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