I got 12/60 on my latest test I want to go over it to figure out what I did wrong and why and how to improve. I was looking if there is anything specific, any pattern to this. When I review my tests I just see all sorts of problems, I forget formulae, I forget basic math, I mess up signs, I run out of time and can't finish the test. Things like that, I don't have an answer key for this test is there any way I can go over it on here and someone else can tell me why I am messing up so much?
There 10 questions and I could probably type them up in under 30 minutes, and another 30 for my work.
Anyways here is the first one. I am supposed to find the derivative of $\log 3 (x+ \sqrt {(x^2-1})$. I then set the problem up as $1/u \ln 3 (1+1/2(x^2-1)^{-1/2}2x)$; this is wrong, completely wrong.
Next questions is let $f(x) = (\cos x)^x$ and find the derivative. I couldn't even do this on the test, I forgot how to get the derivative of a variable that is an exponent, I knew what to do I just couldn't make sense of how to do and I have scrawled down about 30 attempts at nothing.
Doing this now I think what I need to do is rewrite the problem as $e^{\ln u^x}$ and then solve it from there. I could be wrong though.
3) I am supposed to solve this word problem.
A particle moves along a real axis and its location, $s$, is given by $s=t^3-12t^2+36t$ ($s$=feet)
a) find the acceleration at $t=2$ seconds
For this I know that I need to get the derivative and put in $2$ for $t$. Pretty simple, I makes the problem $3t^2-24t+36=0$; I think I forgot to do this one, not sure what happened but this is all I have written down, not sure why. I would plug in $2$ and get $0$, oh I guess I did have the answer written down. It was probably just wrong.
b) When is the particle moving in the positive direction?
I know for this I need to find the critical numbers and test points around them to see where they are increasing or decreasing. I have positive from $5$ to $\infty$.
c) What is the total distance traveled in the first $6$ seconds?
I have written down $39$ ft.
I am not sure what the rules on this are so I will not post anymore questions under this topic unless I know it is okay to. I would like to transcribe the whole test if that is possible.