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March 27th, 2010, 01:29 AM  #1 
Member Joined: Oct 2009 Posts: 50 Thanks: 0  how to calculate the highest slope of a function?
I know you have to calculate f '(x) = 0 to find the extreme value of a function, but how do you know if it's actually the highest slope? I suppose you just have to plot it and see? 
March 27th, 2010, 02:45 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,255 Thanks: 507  Re: how to calculate the highest slope of a function? Quote:
 
March 27th, 2010, 07:04 PM  #3 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 338 Thanks: 4 Math Focus: primes of course  Re: how to calculate the highest slope of a function?
this is what differentiation does, find the extrema. So, if you differentiate one more time, you'll have your answer. For an example, see this page: http://www.worsleyschool.net/science...erivative.html. The first deriv there ends up as 3*x^24*x5. If you differentiate it again (I used WolframAlpha, box input "differentiate 3x2  4x  5" ), the result depicts a little diagram plot where you can see the steepest slope is around x=0.667. You can try surrounding values back into the first derivative and you'll see (0.66,6.3332), (0.67,6.3333), and (0.68,6.332, confirming what the first plot on the website link shows for steepest slope (as much as ones eye can tell). Of course the precise eq'n is 6x4, which gives sol'n as 4/6=0.6666 repeating. The 2nd derivative in this case is simple, but WA tools helps illustrate a bit more visually for this xplanation. 
March 27th, 2010, 09:09 PM  #4 
Member Joined: Oct 2009 Posts: 50 Thanks: 0  Re: how to calculate the highest slope of a function?
ok thanks alot. I admit I wasn't very clear in my formulation. Sorry for that. 

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