anonymous
  • anonymous
Help Please! I don't know how to continue on =(
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
Okay, now calculate the first derivative of what you have in the first box. Can you do that? @Invizen
anonymous
  • anonymous
(x/(3sqrt(x^2)+4))-(1/4)

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anonymous
  • anonymous
\[\frac{ x }{ 3\sqrt{x ^{2} + 4} } - \frac{ 1 }{ 4 } = \frac{ 4x - 3\sqrt{x ^{2} + 4} }{ 12\sqrt{x ^{2} + 4} }\]
anonymous
  • anonymous
You are looking for where the numerator is equal to zero and that is at:\[x = \sqrt{\frac{ 36 }{ 7 }}\]
anonymous
  • anonymous
That's approximately: 2.2677868380553633632870992174051
anonymous
  • anonymous
Are you with me so far, or are you in either disagreement or confusion, @Invizen ?
anonymous
  • anonymous
I'm with you so far!
anonymous
  • anonymous
Cool! This answers part b. Now, you can take that value for x and put it into your equation in part "a", and then you will have an answer for part "c". As for part "d", before calculating the second derivative, which will be a sufficient test for concavity, you can notice that the first derivative goes from negative to positive around that value of "x", showing you that you have minimum (for time, evaluated in terms of "x"). You can do that to determine whether or not you have a max or if you have a min and don't know which one and don't want to do the second derivative. Of course, this problem calls for the second derivative for part "d", but you should be able to get that given what I gave you for the first derivative.
anonymous
  • anonymous
Awesome! Thanks so much! I will finish this!
anonymous
  • anonymous
Well, it's been super working with you! @Invizen
anonymous
  • anonymous
uw! Good luck to you in all of your studies and thx for the recognition! @Invizen
anonymous
  • anonymous
No problem at all!
anonymous
  • anonymous
btw, here's a drawing, but I think you are already past this point:|dw:1370998777630:dw|
anonymous
  • anonymous
And that dotted distance divided by 3 along with that "7-x" divided by 4 is your t(x) time function. But again, you already know that from part a.
anonymous
  • anonymous
Yeah! I drawing the graph and what not was the first thing I did!
anonymous
  • anonymous
Well since you said you will finish this, I'll let you do that unless you think you will have trouble calculating the second derivative, which is all you have left to do. @Invizen It seems to me that you already had a pretty good grasp on this problem. Maybe all I did was slightly organize some of your thinking.
anonymous
  • anonymous
Yeah most problems I encounter I just need to know where I should start - like what's the first step then I usually solve it - because my thinking is based on wording and once the wording for a question is different I get flustered =/
anonymous
  • anonymous
ok, well take care and nice working with you. I have to go help a senior right now, so you should have no real trouble from here on out.
anonymous
  • anonymous
Yeup! Thanks again!

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