
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 18th, 2019, 12:41 AM  #1 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  "Finding Inflection Points" Math Problems Help
I am just learning this new topic at school, and was hoping that you can help me with this example my teacher provided me. The problem is: Let f(x)=2x^48x^3+180x^2. For what values of x does the graph of f have a point of inflection? I understand that you have to do something with the second derivative but I don't remember how to start off the entire process, could anyone please help in explaining and showing each step individually from beginning to end? The problem I had to solve for homework was: Let f(x)=0.5x^46x^327x^2. For what values of x does the graph of f have a point of inflection? The second derivative I got was:6x^236x^154 which equals 6(x+3)(x+3)=0, so the value of x would just be x=3 right? Last edited by skipjack; February 18th, 2019 at 02:48 PM. 
February 18th, 2019, 04:48 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,969 Thanks: 2219 
The first derivative of f(x) is 8x³  24x² + 360x, so its second derivative is 24x²  48x + 360, which equals 24(x + 5)(x  3). Hence the second derivative is zero for x = 5 and for x = 3. The first derivative has a turning point for these values of x, so they're the values of x for which f(x) has a point of inflection. For the homework problem, yes, there's just one inflection point, where x = 3. Correction (thanks, skeeter): x = 3 isn't a point of inflection. The first derivative has a point of inflection, not a turning point, at x = 3. Last edited by skipjack; February 18th, 2019 at 03:01 PM. 
February 18th, 2019, 07:44 AM  #3  
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  Quote:
$f''(x) = 6(x+3)^2 = 0$ at $x=3$ is true, but f''(x) does not change sign there.  

Tags 
derivatives, finding inflection points, inflection points, math, mikeandike, problem, problem solving, problems 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
inflection points analysis  m.nikolov  Calculus  2  January 12th, 2013 02:47 PM 
inflection points  cheyb93  Calculus  4  November 8th, 2012 11:30 AM 
Finding Inflection Points  soulrain  Calculus  5  June 22nd, 2012 05:13 PM 
inflection points questions, help?  mathhelp123  Calculus  2  December 5th, 2009 07:34 AM 
inflection points  stainsoftime  Calculus  3  December 15th, 2008 12:19 AM 