October 25th, 2014, 01:12 PM  #1 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4  Concavity examples?
What does a graph that has an inflection point and is rising everywhere look like? a stretched out S? What does a concave down graph with NO highest point look like? Also, I need to sketch a graph with two inflection points and EXACTLY one place where the tangent line has slope 0. Thank you for your time. Last edited by Omnipotent; October 25th, 2014 at 01:26 PM. 
October 25th, 2014, 01:27 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,737 Thanks: 1387  Quote:
Quote:
 
October 25th, 2014, 01:43 PM  #3 
Member Joined: Sep 2014 From: Cambridge Posts: 64 Thanks: 4 
[QUOTE=skeeter;210468]look at the graph of $\displaystyle y = x^3$ but its not rising at x=0 no? 
October 25th, 2014, 01:54 PM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,737 Thanks: 1387 
[QUOTE=Omnipotent;210472] Quote:
If you're looking for a function with an inflection point where $\displaystyle f'(x) > 0$ for all x, then look at $\displaystyle y = \arctan{x}$  

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