Question

Help Please! I don't know how to continue on =(

Answer 1

Okay, now calculate the first derivative of what you have in the first box. Can you do that? @Invizen

Answer 2

(x/(3sqrt(x^2)+4))-(1/4)

Answer 3

\[\frac{ x }{ 3\sqrt{x ^{2} + 4} } - \frac{ 1 }{ 4 } = \frac{ 4x - 3\sqrt{x ^{2} + 4} }{ 12\sqrt{x ^{2} + 4} }\]

Answer 4

You are looking for where the numerator is equal to zero and that is at:\[x = \sqrt{\frac{ 36 }{ 7 }}\]

Answer 5

That's approximately:

2.2677868380553633632870992174051

Answer 6

Are you with me so far, or are you in either disagreement or confusion, @Invizen ?

Answer 7

I'm with you so far!

Answer 8

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.

Answer 9

Awesome! Thanks so much! I will finish this!

Answer 10

Well, it's been super working with you! @Invizen

Answer 11

uw! Good luck to you in all of your studies and thx for the recognition! @Invizen

Answer 12

No problem at all!

Answer 13

btw, here's a drawing, but I think you are already past this point:

Answer 14

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.

Answer 15

Yeah! I drawing the graph and what not was the first thing I did!

Answer 16

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.

Answer 17

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 =/

Answer 18

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.

Answer 19

Yeup! Thanks again!