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 18:02, 18 February 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 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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