Difference between revisions of "009A Sample Final 3, Problem 9"

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::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
 
::<math>g(x)=(2x^2-8x)^{\frac{2}{3}}</math>
  
<span class="exam">(a) Find all critical points of <math>g</math> over the <math>x</math>-interval <math>[0,8].</math>
+
<span class="exam">(a) Find all critical points of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over the &nbsp;<math style="vertical-align: 0px">x</math>-interval &nbsp;<math style="vertical-align: -5px">[0,8].</math>
  
<span class="exam">(b) Find absolute maximum and absolute minimum of <math>g</math> over <math>[0,8].</math>
+
<span class="exam">(b) Find absolute maximum and absolute minimum of &nbsp;<math style="vertical-align: -4px">g</math>&nbsp; over &nbsp;<math style="vertical-align: -5px">[0,8].</math>
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"

Revision as of 13:38, 6 March 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 g(x)=(2x^2-8x)^{\frac{2}{3}}}

(a) Find all critical points 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 g}   over the  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 x} -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 [0,8].}

(b) Find absolute maximum and absolute minimum 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 g}   over  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 [0,8].}

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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