Simple calculus problem has me frustrated! help

Test Preparation
1

<p>dy/dx=x^3/y^2</p>

<p>y(2)=3</p>

<p>now this seems hecka simple cross multiply integrate and get this:</p>

<p>1/3 y^3 + C = 1/4 X^4</p>

<p>then plug in 2 for y and 3 for x.... and solve... right ?</p>

<p>however college board and I keep getting a different answer...mine isn't even the listed choices...</p>

<p>they say its:</p>

<p>cuberoot(.75x^4 + 15)</p>

<p>i don't get it someone help please this is supposed to be an easy as hell question and i can't even get it right ***!</p>

2

<p>plug in 2 for x and 3 for y and you should get the right answer.</p>

3

<p>Plugging in (2,3) you get C=-5.</p>

<p>1/3<em>y^3-5=1/4</em>x^4
y^3=3/4<em>x^4+15
y=(.75</em>x^4+15)^(1/3)</p>

4

<p>also am i interpreting correctly by
y(2)=3
they mean x=3 when y =2?</p>

5

<p>when they say y(2)=3 that means when x=2 y=3, but I can see how you confused them</p>

6

<p>okay i guess i just had a brain spasm because 10 min later i'm like wt how the hell did i get that wrong... (cuz i tried switching to x=2 y=3 and it
still didn't work)</p>

7

<p>another dumb one:
SEE POST BELOW FOR LINK!</p>

<p>I. The domain of F'(X) is the open interval a,b
II F is continuous on the open interval a,b
III the derivitive of F is positive on interval A,C</p>

<p>now i don't get why I. is false....
II.</p>

8

<p><a href="http://www.collegeboard.com/prod_downloads/ap/students/calculus/ap_cd_calculus.pdf%5B/url%5D"&gt;http://www.collegeboard.com/prod_downloads/ap/students/calculus/ap_cd_calculus.pdf&lt;/a&gt;&lt;/p>

<p>its on page 29</p>

<p>check it out its probably good practice for you too...(some of the questions on there) </p>

<p>also could anyone explain #2 as well??
our calc teacher is really bad she told us just plugin .00001 for h and see what its doing... ... like we can do that on the AP test w/o a calculator lmfao! its her first year teaching calculus and she doesn't really kno that good whats going on..</p>

9

<p>a is false because there is a sharp corner and a function is not differnetiable where there is a corner</p>

<p>b is true because there is no break of continuation of f therefore f' is also always continuous</p>

<p>c is true because f is increasing from a to c, therefore f' is postive from a to c</p>

10

<p>i'm stupid...<br>
how about #2?</p>

<p>thanks btw</p>

11

<h1>2 is the definition of a derivitive (lim h->0 (f(x+h)-f(x))/h ).</h1>

<p>f(x) = cos(x) so f'(x) = -sin(x). For x = 3(pi)/2, f'(3(pi)/2) = -sin(3(pi)/2) = -(-1) = 1</p>

12

<p>i see i see... it's starting to come back thanks</p>