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 <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">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 <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">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 <math>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 <math>y=f(x).</math>
  
 
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'''Solution:'''
 
'''Solution:'''
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Revision as of 18:57, 18 February 2017

Let

(a) Find all local maximum and local minimum values of find all intervals where is increasing and all intervals where is decreasing.

(b) Find all inflection points of the function find all intervals where the function is concave upward and all intervals where is concave downward.

(c) Find all horizontal asymptotes of the graph

(d) Sketch the graph of

Foundations:  


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

Step 1:  
Step 2:  


Final Answer:  
(a)
(b)
(c)

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