Difference between revisions of "009A Sample Final 2, Problem 10"

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::<math>f(x)=\frac{4x}{x^2+1}</math>
 
::<math>f(x)=\frac{4x}{x^2+1}</math>
  
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<span class="exam">(a) Find all local maximum and local minimum values of <math>f,</math> find all intervals where <math>f</math> is increasing and all intervals where <math>f</math> is decreasing.
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<span class="exam">(a) Find all local maximum and local minimum values of &nbsp;<math style="vertical-align: -4px">f,</math>&nbsp; find all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is increasing and all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is decreasing.
  
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<span class="exam">(b) Find all inflection points of the function <math>f,</math> find all intervals where the function <math>f</math> is concave upward and all intervals where <math>f</math> is concave downward.
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<span class="exam">(b) Find all inflection points of the function &nbsp;<math style="vertical-align: -4px">f,</math>&nbsp; find all intervals where the function &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is concave upward and all intervals where &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; is concave downward.
  
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<span class="exam">(c) Find all horizontal asymptotes of the graph <math>y=f(x).</math>
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<span class="exam">(c) Find all horizontal asymptotes of the graph &nbsp;<math style="vertical-align: -5px">y=f(x).</math>
  
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<span class="exam">(d) Sketch the graph of <math>y=f(x).</math>
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<span class="exam">(d) Sketch the graph of &nbsp;<math style="vertical-align: -5px">y=f(x).</math>
  
 
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!Step 2: &nbsp;
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|'''(c)'''
 
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[[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Revision as of 13:55, 6 March 2017

Let

(a) Find all local maximum and local minimum values of  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f,}   find all intervals where  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}   is increasing and all intervals where  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}   is decreasing.

(b) Find all inflection points of the function  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f,}   find all intervals where the function  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}   is concave upward and all intervals where  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f}   is concave downward.

(c) Find all horizontal asymptotes of the graph  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(x).}

(d) Sketch the graph of  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=f(x).}

Foundations:  


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

Step 1:  
Step 2:  
(d):  


Final Answer:  
(a)
(b)
(c)
(d)

Return to Sample Exam

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