May 15th, 2016, 10:09 PM  #1 
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1  Local Minima and Local Maxima
Hello, How can determine local minima and local maxima in under graph? Thanks 
May 16th, 2016, 09:51 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,741 Thanks: 710 
Do you not know what "local minima" and "local maxima" mean? A point on an xy graph is a "local minimum" if and only if The yvalue at that point is lower than that of points in some small interval around it. On this graph the point at what looks like (30, 4000) (we can only estimate those values, of course) is not just a "local" maximum but a "global" maximum. It also looks like (40, 600) is a local maximum but that's more subtle. Similarly, it looks like (51, 500) is a local minimum. There are, of course, several more. If you are looking for a way of calculating precise values from this graph, there are none. Look at the graph and pick points that appear to be higher (or lower) than points immediately around them.

May 16th, 2016, 10:42 AM  #3  
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1  Quote:
Why we haven't local maximum? How can calculate these feature with formula? What are formula? Thanks  
May 16th, 2016, 11:35 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 
Do you have a function that models the graph, or is this just a plot of connected data points?

May 16th, 2016, 12:14 PM  #5 
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1  
May 16th, 2016, 01:01 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319  There are numerical methods to determine extrema of data plots as discussed at the link ... Finding Local Extrema » File Exchange Pick of the Week 
May 16th, 2016, 01:58 PM  #7  
Senior Member Joined: Feb 2014 Posts: 112 Thanks: 1  Quote:
If we suppose a function that models the graph,now how can determine?  
May 16th, 2016, 03:34 PM  #8 
Math Team Joined: Jul 2011 From: Texas Posts: 2,640 Thanks: 1319 
Good question ... given the graph's behavior, I imagine it wouldn't be easy.


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