2011 AP AB Calculus Ch. 3 (Derivatives)

Whatever you share, be sure that it is relevant!

2011 AP AB Calculus Ch. 3 (Derivatives)

9/19/2011

Be a team player and help out your peers! Ask AND answer questions so that everyone may benefit.

Honsu Kim

9/19/2011 09:03:04 am

Does anyone understand the graphs at all?

Ryan Pape

9/19/2011 11:50:29 am

Yes, you find the derivative of f(x), I'm assuming that #7 is f(x) = x^2, 8 is x^3, 9 is cosx, and 10 is x^4. So instead of plugging a point you just put in x's and h's. Then, you'll have an equation at the end. Say the equation is 2x. You would look for the graph of 2x (letter b) and make it the answer of the corresponding number. Does anyone know how to do number 9 though? I can't figure out how to get h out of cos(x+h)-cos(x)/h

Ryan Pape

9/19/2011 12:41:47 pm

Psych, number 10's regular function graph is actually f(x) = something . . don't know what
sorry

vasishta Angara

9/19/2011 12:58:32 pm

For number 1
all u do is is plug in f(2) into the equation and have the equation = 5 right?

Kelsey Cyr

9/19/2011 02:01:07 pm

I'm confused on number one, I think you plug in f(2) for (x) and have the equation = 5, but I don't think it gives you the right answer.

Courtney Lynch

9/19/2011 03:51:06 pm

for number one a. use the fact that the derivative of a point is the slope at that point. So, you have the slope of a line and a point is passes through (f(2)=3 is the point)
b. look back to the last section of ch. 2

Kelsey Cyr

9/19/2011 03:58:10 pm

Thanks Court, that makes more sense now!

Dan Karesh

9/20/2011 01:34:09 am

how do you do number 15 if they don't give you an actual equation?

heli bhatt

9/20/2011 09:32:56 am

how do you do #17 ?

vasishta Angara

9/20/2011 11:07:12 am

Dan for #15, i think they're asking us to estimate.

Courtney Lynch

9/20/2011 12:30:11 pm

Dan, for #15 you look at the graph, notice it is going from convex to concave. Since you know the slope is 0 aroung Junuary 1 and July 1 the middle of that has to have the greatest slope. And than to find the slope take the y values from March 15-April 15 and divide it by the x values, the number of days in a month (30).
If you understand a., i think b and c should become a little easier.

Courtney Lynch

9/20/2011 12:42:43 pm

Heli, for #17 a. you look at the top graph and see where its y-values are the highest (40,2200) and the lowest (150,100). After that look at the bottom graph, find those two x-values and notice where they are located (what is the y-value).
b. look at the bottom graph first. notice where the highest part of the graph is (20,40) and the lowest part of the graph (65,-55). than look at the top graph, use the x-values you found to figure out what the y-values of the top graph are and those would be your answers.

Dan Karesh

9/20/2011 03:06:50 pm

got it! thanks!

Brianne Honda

9/21/2011 12:24:38 pm

What is NDER...

Andrew Fox

9/21/2011 03:10:55 pm

NDEr is the numerical derivative of f. it shows this on page 108. for # 27 how is the answer tan(x)?

Ryan Pape

9/21/2011 03:19:56 pm

Brianne,
A way of estimating the derivative of something within 3 decimal places. It stands for numerical derivative and it's the limit of f(a+h) - f(a-h)/2h as h approaches .001
If you see NDER (2x^2, 3) it means the numerical derivative of 2x^2 when x = 3. Just plug in x and h (.001)

Ryan Pape

9/21/2011 03:20:28 pm

Haha, I need to refresh my page, sorry Andrew

Vasishta Angara

9/22/2011 10:48:11 am

For #5 I tried using the quotient rule but then I ended up getting a really weird answer. Did anyone else use the rule and get the right answer??

Vasishta Angara

9/22/2011 10:54:17 am

Ooops nvm. I didn't apply the rule correctly. i got it now

Kelsey Cyr

9/22/2011 10:59:58 am

for #15, you use the quotient rule right? Or do you have to use the product rule first for the top, then the quotient rule?

Whitney Pike

9/22/2011 11:11:50 am

Yeah so i tried 11 twice and for some reason i came up with two different answers (like for a and b) both times... is there anyway i can just like see the process someone else used?

Vasishta Angara

9/22/2011 11:31:42 am

Kelsey: Yea for #15 i simplified the top first and then i used the quotient rule.

Whitney: What did u get for A and B??

Kelsey Cyr

9/22/2011 11:34:33 am

Vashista, Okay that's what I did, but i got a different answer than what the book says you're supposed to get... did thta happen to you? or did i mess up somewhere? Cause i did it twice... ?

Vasishta Angara

9/22/2011 11:36:44 am

Ohh srry. i didn't check the answer yet.
hmmm. Im gonna try it again and then ill try it the other way

Kelsey Cyr

9/22/2011 11:37:54 am

p.s. I'm so sorry I just realized I spelled your name wrong, sorry Vasishta

Vasishta Angara

9/22/2011 11:38:37 am

LOL its ok

Vasishta

9/22/2011 11:41:34 am

Yea i have no idea for #15.
its not working either way ...

Kelsey Cyr

9/22/2011 11:56:17 am

Yeahh, and I'm having the same problem for 19 also... Does anyone else know how to do it if its not those?

Mrs. Johnson

9/26/2011 05:46:31 am

@Kelsey@Vasishta:
For number 15, multiply the numerator out and get x^3-1, still divided by the denominator x^3. You have a achoice from there to either rewrite the equation as two terms: 1-x^-3 and take the derivative of it OR you can leave it as a quotient and apply the quotient rule. Either way you will ge the same result.

Nice job blogging guys! Keep it going!

Mrs. Johnson

9/26/2011 05:48:34 am

@Kelsey:
The same concept applies for #19. You may choose to multiply the numerator out and then do the same for the denominator and then apply the quotient rule. Be sure to list what you call u, v, u', v' so that making corrections will be made easy.

heli bhatt

9/26/2011 09:42:38 am

how do you do #15 and #16 from derivative worksheet ?

Vasishta

9/26/2011 10:33:30 am

Heli: For number 15 u have to use the power rule. So u would have

3ax^2 + 2bx + 1.

heli bhatt

9/28/2011 08:40:02 am

how do you do #15 from 3.4 ?

Dan Karesh

9/28/2011 11:46:19 am

can anyone explain how to do 28 29 and 31? i get everything for the most part but how to do those?

Kelsey Cyr

9/28/2011 01:34:07 pm

Dan,
For 28, It's jsut writing like explaining why each graph is which. It's all derivatives, and if you remember the power rule you know which graph looks like a cubic, parabola, and linear. The cubic has the highest power so it is the first graph. It correlates with position, velocity and acceleration. So like which one of those is first, then its derivative, then the derivative of that.

Bakir Baker

9/28/2011 02:34:43 pm

Dan, for 29, if you look at C, you know that the derivative of C looks like B, and the derivative of B looks like A.

C is position (x^3)
B is velocity (2x^2)
A is acceleration (4x)

Dan Karesh

10/3/2011 10:59:14 am

Can anyone explain the chain rule because I am so lost

Kelsey Cyr

10/3/2011 11:15:56 am

for # 24 for 3.6, do we just use the chain rule? or is it like the product rule for both parts of the equation?

Courtney Lynch

10/3/2011 03:46:16 pm

Kelsey
For #24 you use the chain rule just like you did in #21.

Whitney Pike

10/8/2011 07:08:47 am

so for number 17 can someone explain it? having y as the argument is confusing me the problem's x= tan y

Vasishta Angara

10/15/2011 06:12:44 am

For number 6 on the worksheet.
Should i leave the 4x^3y on the left or subtract it over?

sam jones

10/17/2011 11:31:06 am

can someone please tell me what assignment we're on? i was out sick today

kelsey C

10/17/2011 02:05:45 pm

sam, 3.8 p. 162, 1-17 odd.

Dan Karesh

10/20/2011 10:49:51 am

This might be a really stupid question, but how do we know when to use the formal or alternate derivative definition?

Courtney Lynch

10/20/2011 11:59:27 am

Just like in one of our warm ups today. It will tell you in the instructions if you have to use the formal derivative definition.

Dan Karesh

10/20/2011 01:11:42 pm

But what if it doesn't? And don't you use the alternate one for points?

Comments are closed.

2011 AP AB Calculus Ch. 3 (Derivatives)

Blog Spot

Author

Archives

Categories