Post Number Two

So everyone, the second week of calculus is over. Of course it's gotten harder, but not everything in life comes easily right? I felt good at the beginning of the week because we were reviewing quotient rule and product rule. Though at the time of learning them I thought those were impossible, I'm now wishing that we were back to that again. I'm confused about everything overall, but there are some things that I did understand this week (Thank God).

For example, I caught on to horizontal tangent points real quick. All you do is find the derivative of the problem given then set equal to zero and solve for x. We were drilled on solving for x last year, so I felt extremely comfortable doing that. An example problem of this is Find the points where y has horizontal tangents y=3x^3 + 4x^2 + 5. Therefore, y'=9x^2 + 8x because you just take the simple derivative of a polynomial. Once finding the derivative, set equal to zero giving you 9x^2 + 8x = 0. Factor out an x giving you x(9x + 8) = 0. You then find that your x points are 0 and -8/9. Next, you must plug in your x's to the original equation in order to find your ys. 3(0)^3 + 4(0)^2 + 5 and 3(-8/9)^3 + 4(-8/9)^2 + 5. These come out to give you the points (0,5) and (-8/9, 6.053). Box it off and that's your answer :)

Also, i understood the arc problems until we got to problems like #53 y=1/2(1/2ln x+1/x-1 + arctanx). I'm not exactly sure what you do first because there's a natural log and an arc formula. If anyone can direct me on this it'd be greatly appreciated.

I still remember the log properties from advanced math so I do okay on those problems. I also do fine on natural log problems unless they have more than one function in it. Like I said I get extremely lost then and have no idea where to start. Basically, I'm doing fine in this class except when it gets to the simplifying parts. I know it's just algebra but I just can't seem to grasp how to do all the right cancellations. I'm sure it'll take a lot of practice which I'm working on but it's just so frustrating not getting it time after time.

Finally, I want to extend the offer to arrange a study group before Wednesday to prepare for the test. I can always use a lot of help so if anyone is interested please let me know because I believe we can all help each other if we work together.

Overall, i'm looking forward to another stressful week full of work and headaches in Calculus--SIKEEEEEEE.