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March 27th, 2010, 01:29 AM   #1
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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?
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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?
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March 27th, 2010, 07:04 PM   #3
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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.
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March 27th, 2010, 09:09 PM   #4
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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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