Can someone explain the process of this problem?

[BillTheButcher]

I am posting here because this is NOT homework. Problems are finished. However we have an exam on friday for calculus 1 class and well... I've been trying real hard to understand it but professor has a real strong accent and he speaks too low, no one can hear a thing!

Anyway, we did the review and I was wondering if someone would explain how he got to those solutions... I marked the parts that I especially don't understand... we will also be allowed to have notes on the exam, so any formulas that you think might help me, or anything at all, will be of great help if you tell me.

There are 5 problems, and if a problem didn't fit in one page, I marked the photo as "Problem 5-a; Problem 5-b" for example. The last problem (problem 5) didn't fit so the link to the pictures are here:

http://img600.imageshack.us/img600/592/lxkk.jpg

http://img28.imageshack.us/img28/4107/fkdt.jpg

I hope you guys can clarify these things to me since the professor who is getting paid to do that, didn't. And yes, I did go to his office hours.

 

[Office_Shredder]

It's really hard to read some of those pages... it would be a lot easier if you typed up the question and what about the solution confused you.

 

[BillTheButcher]

Problem 1:

The position of a body moving on a coordinate line is given by S = t2 - 4t + 4, with S as meters and t as seconds. When, if ever, during the interval 0 <_ t<_ 4 does the body change direction?

Here I just don't know how we get from "S = t2 - 4t + 4" to "V=ds/dt = 2t - 4.

Problem 2:

The size of a population of lions after 't' months is given by P=100(1+0.2t+0.02t2=. Find the growth rate when P=2500.

Here, I don't understand at the end of the Problem 2-b picture, why is the solution t=30 months when in our calculations we had (t+40)(t-30)=0. Why let '40' out and use only '30' as an answer?
In the same problem, I don't understand how he got from multiplying that equation times 100 which resulted in =100+20t+2t2 to dP/dt=20+4t?

I don't get those sketches in problem 3.

In problem 4, in next to last line, I don't get how he got from y=3x+2+x-1+x-2 to y' = 3-x-2-2x-3.

As for problem 5, starting the 2nd I don't know how he got there.

 

[jbunniii]

Problem 1:

The position of a body moving on a coordinate line is given by S = t2 - 4t + 4, with S as meters and t as seconds. When, if ever, during the interval 0 <_ t<_ 4 does the body change direction?

Here I just don't know how we get from "S = t2 - 4t + 4" to "V=ds/dt = 2t - 4.

Can you clarify what you don't understand? Is it that you don't recognize that the derivative of $t^2 - 4t + 4$ is $2t - 4$, or that you don't see how this applies to this problem?

The size of a population of lions after 't' months is given by P=100(1+0.2t+0.02t2=. Find the growth rate when P=2500.

Here, I don't understand at the end of the Problem 2-b picture, why is the solution t=30 months when in our calculations we had (t+40)(t-30)=0. Why let '40' out and use only '30' as an answer?

Well, I can't read your images very well (one of them is even upside down!), but first you need to find $t$ for which $P(t) = 2500$. So we need to solve $100(1 + 0.2t + 0.02t^2) = 2500$, or equivalently, $t^2 + 10t -1200 = 0$. The polynomial on the left hand side factors as $(t-30)(t+40)$, so equation reduces to $(t-30)(t+40) = 0$. This is true if $t = 30$ or $t = -40$. So it's not $40$ which is being excluded as a solution, but $-40$. This is presumably because the formula given for $P(t)$ is only meant to be valid for positive values of $t$. So $t=30$ is the only solution that makes sense in this context.

In the same problem, I don't understand how he got from multiplying that equation times 100 which resulted in =100+20t+2t2 to dP/dt=20+4t?

Again, are you asking why the derivative of $100 + 20t + 2t^2$ is $20 + 4t$? This is a very elementary derivative! Surely you must have seen other examples like this?

I don't get those sketches in problem 3.

In problem 4, in next to last line, I don't get how he got from y=3x+2+x-1+x-2 to y' = 3-x-2-2x-3.

As for problem 5, starting the 2nd I don't know how he got there.

Please write out the questions. Your images are too painful to read. Also, it is preferable to start a separate thread for each question, unless they are closely related.

 

[jbunniii]

Also please note that even if this is not homework, it still belongs in the homework forums. See the pinned note at the top of this forum:

https://www.physicsforums.com/showthread.php?t=44101