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

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<span class="exam">(d) Sketch the shape of the graph of &nbsp;<math style="vertical-align: -4px">f.</math>
 
<span class="exam">(d) Sketch the shape of the graph of &nbsp;<math style="vertical-align: -4px">f.</math>
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[[009A Sample Final 3, Problem 6 Solution|'''<u>Solution</u>''']]
  
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!Foundations: &nbsp;
 
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|'''1.''' <math style="vertical-align: -5px">f(x)</math>&nbsp; is increasing when &nbsp;<math style="vertical-align: -5px">f'(x)>0</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is decreasing when &nbsp;<math style="vertical-align: -5px">f'(x)<0.</math>
 
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|'''2. The First Derivative Test''' tells us when we have a local maximum or local minimum.
 
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|'''3.''' <math style="vertical-align: -5px">f(x)</math>&nbsp; is concave up when &nbsp;<math style="vertical-align: -5px">f''(x)>0</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; is concave down when &nbsp;<math style="vertical-align: -5px">f''(x)<0.</math>
 
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[[009A Sample Final 3, Problem 6 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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'''Solution:'''
 
  
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'''(a)'''
 
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!Step 2: &nbsp;
 
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!Final Answer: &nbsp;
 
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[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 16:42, 2 December 2017

Let

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

(b) 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 f}   and test each for local maximum and local minimum.

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

(d) Sketch the shape of 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 f.}

Solution


Detailed Solution


Return to Sample Exam

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