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July 16th, 2017, 03:55 PM  #1 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0  Curve Sketching Concavity questions
1. Test f(x)=−8x^4−5x^3+7 for concavity and inflection points. Solution: f has inflection points when x=____ and x=____. (List the smaller value first.) f is concave down on (−infinity,_____) U (_______, infinity) and its concave up on (_____,_______). 2. Test the function g(x)=(−8x^3) − (−132)x^2 + (−576)x− 5 for relative maximum and minimum. Use the secondderivative test if possible. Solution: From g'(x)= Drop down menu with following options (pick one) [(8x^2)(132)x +(576)], [(24x^2)(132)x + (576)], [(24x^2)(264)x + (576)] it follows that the critical values of g are x1= ____and x2=_____ . (List the smaller value first.) Since g''(x)= drop down menu [(48x)(132)], [(48x)(264)] we have that g"(x1)=_____ when ( >0 OR <0) and g"(x2)= ________ when ( >0 OR <0) Therefore, by the secondderivative test, there is a (relative minimum OR relative maximum) when x=x1. and there is a (relative minimum OR relative maximum) when x=x2. Thanks so much. 
July 16th, 2017, 04:07 PM  #2 
Senior Member Joined: Oct 2009 Posts: 142 Thanks: 60 
Any thoughts? Do you know how to find inflection points?

July 16th, 2017, 04:07 PM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,662 Thanks: 1327 
1) for any polynomial function, inflection points occur where f''(x) changes sign ... that would mean you would first have to find where f''(x) = 0 2) a polynomial function has a maximum where f'(x) = 0 and f''(x) < 0 ... a minimum where f'(x) = 0 and f''(x) > 0 
July 16th, 2017, 04:44 PM  #4 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0 
so for question one, i dound that the second derivative is 96x^230x and when setting that to equal 0 I got 30/96 =x. Is that correct?

July 16th, 2017, 04:51 PM  #5  
Math Team Joined: Jul 2011 From: Texas Posts: 2,662 Thanks: 1327  Quote:
Quote:
$f''(x) = 96x^2  30x = 6x(16x + 5) = 0$ there are two solutions for $x$ ...  
July 16th, 2017, 05:53 PM  #6 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0 
x=6 and x=5/16 ?

July 16th, 2017, 06:10 PM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 2,662 Thanks: 1327  
July 16th, 2017, 08:49 PM  #8 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0  
July 16th, 2017, 11:21 PM  #9 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0 
So... I got it thanks for all the help. For the second equation just find the first derivate and its x values there will be 2 of them. Then find the second derivaive and take your x1 and x2 and plug those in. You should get 2 numbers and one will be greater than 0 and the other less than 0.


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concavity, curve, questions, sketching 
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