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

From Grad Wiki
Jump to navigation Jump to search
Line 2: Line 2:
 
::<math>f(x)=\frac{4x}{x^2+1}</math>
 
::<math>f(x)=\frac{4x}{x^2+1}</math>
  
−
::<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.
+
<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.
  
−
::<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.
+
<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.
  
−
::<span class="exam">c) Find all horizontal asymptotes of the graph <math>y=f(x).</math>
+
<span class="exam">(c) Find all horizontal asymptotes of the graph <math>y=f(x).</math>
  
−
::<span class="exam">d) Sketch the graph of <math>y=f(x).</math>
+
<span class="exam">(d) Sketch the graph of <math>y=f(x).</math>
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
Line 21: Line 21:
 
|
 
|
 
|}
 
|}
 +
  
 
'''Solution:'''
 
'''Solution:'''
Line 89: Line 90:
 
|
 
|
 
|}
 
|}
 +
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 17:57, 18 February 2017

Let

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(x)=\frac{4x}{x^2+1}}

(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:  


Final Answer:  
(a)
(b)
(c)

Return to Sample Exam

Retrieved from "https://gradwiki.math.ucr.edu/index.php?title=009A_Sample_Final_2,_Problem_10&oldid=2598"