1. Consider the function g(x) =. ex (a) Determine the domain of the function g. (b) Find all horizontal and vertical asymptotes of g. For each asymptote you find, write down a limit (or two one-sided limits) which describe the asymptote. (c) Find the values of x where gʻ(x) = 0 or g'(x) does not exist. (Hint: There are two.) (d) Find the intervals where g is increasing and decreasing. Give all local maximum and minimum points. (e) Find the intervals where g is concave up and concave down. Does g have an inflection point? Explain why or why not. (f) Use the information you have found in the previous parts to sketch a graph of y = g(x).
1. Consider the function g(x) =. ex (a) Determine the domain of the function g. (b) Find all horizontal and vertical asymptotes of g. For each asymptote you find, write down a limit (or two one-sided limits) which describe the asymptote. (c) Find the values of x where gʻ(x) = 0 or g'(x) does not exist. (Hint: There are two.) (d) Find the intervals where g is increasing and decreasing. Give all local maximum and minimum points. (e) Find the intervals where g is concave up and concave down. Does g have an inflection point? Explain why or why not. (f) Use the information you have found in the previous parts to sketch a graph of y = g(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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Transcribed Image Text:1. Consider the function g(x) =.
ex
(a) Determine the domain of the function g.
(b) Find all horizontal and vertical asymptotes of g. For each asymptote you find, write
down a limit (or two one-sided limits) which describe the asymptote.
(c) Find the values of x where gʻ(x) = 0 or g'(x) does not exist. (Hint: There are two.)
(d) Find the intervals where g is increasing and decreasing. Give all local maximum and
minimum points.
(e) Find the intervals where g is concave up and concave down. Does g have an inflection
point? Explain why or why not.
(f) Use the information you have found in the previous parts to sketch a graph of
y = g(x).
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