Difference between revisions of "009A Sample Final 1, Problem 10"

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<span class="exam">Consider the following continuous function:
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::::::<math>f(x)=x^{1/3}(x-8)</math>
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<span class="exam">defined on the closed, bounded interval <math>[-8,8]</math>.
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::<span class="exam">a) Find all the critical points for <math>f(x)</math>.
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::<span class="exam">b) Determine the absolute maximum and absolute minimum values for <math>f(x)</math> on the interval <math>[-8,8]</math>.
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Foundations: &nbsp;  
 
!Foundations: &nbsp;  

Revision as of 20:26, 1 February 2016

Consider the following continuous 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(x)=x^{1/3}(x-8)}

defined on the closed, bounded interval 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 [-8,8]} .

a) Find all the critical points for 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)} .
b) Determine the absolute maximum and absolute minimum values for 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)} on the interval 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 [-8,8]} .
Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  
Step 3:  

(c)

Step 1:  
Step 2:  
Final Answer:  
(a)
(b)
(c)

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