<p>You’re right when you say that the denominator being 0 will make dy/dx undefined. So, you just solve the numerator for the values where the top is 0.</p>
<p>The top is the derivative of y with respect to t (I’ll call it y’).<br>
y=2t^3 - 3t^2 - 12t</p>
<p>y’=6t^2 - 6t - 12</p>
<p>Factor out a 6 and set it equal to 0</p>
<p>y’= 6(t^2 - t - 2) = 0</p>
<p>The 6 divides away and you’re left with t^2-t-2 = 0</p>
<p>Factor: (t+1)(t-2)</p>
<p>t = -1 and 2</p>
<p>D) -1 and 2 only</p>
<p>alright, for that question, both dx/dt and dy/dt have to equal 0 for the particle to be at rest.
dx/dt = 3t(t-2)
dy/dt = 6(t-2)(t+1)
So, obviously t=2 makes both of the above 0, but when t=-1, the y value is not changing, but the x value is, and vice versa for t=0. Does that make sense?</p>
<p>oh so BOTH derivatives have to be 0 at the same time?
i see i see
thanks =)</p>
<p>yes, dx/dt is horizontal movement while dy/dt is vertical movement. You found the places where the object was only moving horizontal, just not moving vertical at all.</p>
<p>Hey you guys are all in calc bc so i have a question. Say i have the chance to test past algebra 2, making it so i would take calc bc junior year. who here is taking calc bc junior year and how do you think it effects chances of acceptance at top schools?</p>
<p>i’m currently a junior
but that would make your yr hectic, if you dont have a decent teacher
because the whole year i thought what my teacher taught us was really good, and that we’ve always been ahead of everyone else, but really, you need to do thousands of problems on your own to really get it.
also, take it only if you know you can get a really high grade in the class so that it doesnt drop your average, since colleges look at it</p>
<p>I’m a sophomore in Calculus BC and I tested out of Algebra II my freshman year. I would definitely recommend testing out of Algebra II and going straight to Precalculus and then BC junior year (I assume that’s your plan). Algebra II and Precalculus curriculum is very similar, so I don’t see the need of spending 2 years on it, especially if you’re good at math.</p>
<p>If you have a solid math foundation and know that your school’s Calculus BC teacher is good, I would recommend you test out of Algebra II.</p>
<p>wow my school doesn’t even allow that…
i self-studied precalc my freshman year but my school wouldn’t give me a placement test into calc for sophomore year, so i was stuck in it for another year…
and i agree with 314159265</p>
<p>Yeah thanks for the advice guys. I figured since geometry didn’t challenge me at all, algebra 2 wouldn’t either but i don’t know what starting highschool with precalc will be like. Anyway, what math are you going to take in your remaining years of highschool?</p>
<p>I’m a junior and didn’t get to test out of anything…we don’t have that at my school. However, we’re on block scheduling so I had AP calc ab first semester and self-studied the bc parts this semester. And as for your last question, I don’t know what math I am going to do next year. I’m planning on self-studying the physics C tests, but my school doesn’t offer much more except stats, which is a joke at my school.</p>
<p>Oh yeah my school has stats as a class too. To me it seems weird to build up a large knowledge of math over the years and finish it off with a class on statistics…i don’t think there are other options except for local community college.</p>
<p>i’m gonna try to start a club for differential equations or other advanced college-level math along with AP stat…it’s so boring, imo (stat, that is)</p>
<p>yeah good idea. as long as there are enough kids willing to do something like that (at least at my school), it would be a great math-type club.</p>
<p>My school is full of dumbasses. Period.</p>
<p>so is mine, but all you need is to find ~20 out of the dumbasses who are not lazy enough to pick up a pen and sign their name on a petition, just to create the club
from then on they could quit if they want to, but as long as the club still exists, you’re fine =)
[and a good teacher]</p>
<p>My advice would be to go to community college and take math courses there. Then maybe your school will have no choice but to let you bypass certain courses. After all, anything at the college level is more difficult.</p>
<p>i tried that with physics, didn’t help =</p>
<p>What are all values of x for which the series SUM 1–>Infinity((x-3)^n)/((n^2)*(5^n)) converges? </p>
<p>A) [-2,8]
B) (-2,8]
C) [-2,8)
D) [-5,5]
E) [-5,5)</p>
<p>I found this problem pretty difficult…Any ideas??</p>
<p>I got the answer as A. </p>
<p>Reasoning:
First, use the ratio test to find which of the two intervals is correct. Ratio Test gives:
|(x-3)/5|<1
or -2<x<8</p>
<p>Now check the endpoints. -2 gives you ((-5)^n)/((n^2)(5^n)) or simplified, ((-1)^n)/(n^2), which converges due to the Alternating Series Test(limit of a = 0 and the terms are decreasing). 8 gives you (5^n)/((n^2)(5^n)) or 1/(n^2) which converges because p (the exponent on the n in the denominator)>1</p>
<p>Therefore, the series converges at both endpoints, leaving the answer at [-2,8].</p>
<p>Thanks that makes sense. I got to finding -2 and 8 as endpoints, but didn’t know what to do after that.</p>