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July 24th, 2012, 05:00 PM   #1
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Derivative at extremum

Here is a problem I can't figure out how to work. I will post the problem in question, and then I will post the steps I completed so far. Between my notes, the video, and internet sources, I can't figure out what to do next

Find the value of the derivative (if it exists) at the indicated extremum.

(-2/3 , 10(root3)/9)

f(x) = -5x (rootx+1)

fprime (-2/3) = _________

Here's what I've done so far:

(x^2+7)(2x) - (x^2)(2x) / (x^2+1)^2

2x^3+14x-2x^3 / (x^2+7)^2 = 14x / (x^2+7)^2

(-5x)(x+1) ^1/2

=(-5x) * 1/2(x+1)^-1/2 + (root x+1)(-5)

Pretty much don't know what to do next. I got this far by watching a video of a similar problem, but have no way to tell if I'm doing this right, since the video skips so many steps with no explanation as to how they got the values they're displaying.
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July 24th, 2012, 06:09 PM   #2
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Re: Derivative at extremum

If I read that right, it's asking for the value of the derivative at a maximum or minimum value, and not at -infinity or +infinity. In that case it will be zero no matter the function.
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July 24th, 2012, 06:12 PM   #3
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Re: Derivative at extremum

Thanks, I appreciate that. This class is a living nightmare lol. Somehow I'm still hanging on though.
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July 24th, 2012, 06:49 PM   #4
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Re: Derivative at extremum

Quote:
Originally Posted by jkh1919
Thanks, I appreciate that. This class is a living nightmare lol. Somehow I'm still hanging on though.
It's no problem. Each person has their own strengths. I'm decent with Calculus and problem solving and I like helping people out with it.
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