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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
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Re: how to calculate the highest slope of a function?

Quote:
 Originally Posted by questioner1 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?
Your question is a little confusing. f'(x)=0 means the slope is zero. What are you looking for when you ask about highest slope?

 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^2-4*x-5. 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 6x-4, 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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