Difference between revisions of "009A Sample Final 3, Problem 6"

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::<math>f(x)=4+8x^3-x^4</math>
 
::<math>f(x)=4+8x^3-x^4</math>
  
<span class="exam">(a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?  
+
<span class="exam">(a) Over what &nbsp;<math style="vertical-align: 0px">x</math>-intervals is &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; increasing/decreasing?  
  
<span class="exam">(b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
+
<span class="exam">(b) Find all critical points of &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; and test each for local maximum and local minimum.
  
<span class="exam">(c) Over what <math>x</math>-intervals is <math>f</math> concave up/down?
+
<span class="exam">(c) Over what &nbsp;<math style="vertical-align: 0px">x</math>-intervals is &nbsp;<math style="vertical-align: -4px">f</math>&nbsp; concave up/down?
  
<span class="exam">(d) Sketch the shape of the graph of <math>f.</math>
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<span class="exam">(d) Sketch the shape of the graph of &nbsp;<math style="vertical-align: -4px">f.</math>
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 14:30, 6 March 2017

Let

(a) Over what  -intervals is    increasing/decreasing?

(b) Find all critical points of    and test each for local maximum and local minimum.

(c) Over what  -intervals is    concave up/down?

(d) Sketch the shape of 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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