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

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<span class="exam"> Let
 
<span class="exam"> Let
  
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::::<math>f(x)=4+8x^3-x^4</math>
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::<math>f(x)=4+8x^3-x^4</math>
  
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::<span class="exam">a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?  
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<span class="exam">(a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?  
  
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::<span class="exam">b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
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<span class="exam">(b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
  
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::<span class="exam">c) Over what <math>x</math>-intervals is <math>f</math> concave up/down?
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<span class="exam">(c) Over what <math>x</math>-intervals is <math>f</math> concave up/down?
  
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::<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 <math>f.</math>
  
 
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'''Solution:'''
 
'''Solution:'''
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Revision as of 19:02, 18 February 2017

Let

(a) Over what -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} 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.}

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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