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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|'''(d)'''
 
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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 14:55, 6 March 2017

Let

(a) Find all local maximum and local minimum values of    find all intervals where    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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