AP Calculus AB and BC Unit 4 Review [Contextual Applications of Differentiation]
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- Опубликовано: 21 июл 2024
- ► My AP Calculus AB and BC Ultimate Review Packets:
AB: bit.ly/KristaAB
BC: bit.ly/KristaBC
Before you watch this video all about Unit 4 of AP Calculus AB/BC, Contextual Applications of Differentiation, make sure you get the study guide that goes with it. The study guide is part of the Ultimate Review Packet, which I made to help you study for AP Calculus AB and BC. It has summary videos, study guides, and practice questions, for every unit, plus AP practice exams.
Skip to section:
0:00 - Introduction
0:50 - 4.1 Interpreting the Meaning of the Derivative in Context
6:09 - 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
13:04 - 4.3 Rates of Change in Applied Contexts Other Than Motion
17:01 - 4.4 Introduction to Related Rates
25:55 - 4.5 Solving Related Rates Problems
32:26 - 4.6 Approximating Values of a Function Using Local Linearity and Linearization
39:35 - 4.7 Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
43:47 - Summary
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If you could use some extra help with your math class, then check out my website // www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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Who's ready for RELATED RATES?!! 🙃
Nooooo. I just don't get it and I live math
Related rates is super tough!! 😬
Taking calc 4 and DiffEQ currently, and related rates is still my least favorite section I’ve ever had to do.
:(((( save me
CORRECTION FOR 4.2: 11:33
To find average velocity over an interval, use the avg rate of change formula for the position equation. To find average acceleration, use the avg rate of change formula for the velocity equation.
That is why the answer for average velocity was six. The acceleration at any point in the equation is 6, so the average acceleration between any two point will always be six. Not 0.
These videos are very useful for someone trying to refresh their memory a few days before the test. Much appreciated.
That’s me right now haha
That’s me hours before💀
My teacher made units 4+5 one test so I had to deal with related rates AND optimization
One of the best teachers I've ever seen for mathematics
Im a math major, who Aces all my tests, but never really understood, what was going on in the problem or what the topic was really about besides just problem solving. This video REALLY helped me out so much to figure out what really is happening behind the math. Thank you so much. This really helped me out a lot and will definitely help me out in the long run. Again Thank You!!! You are AMAZING
krista👑 👍👋
I'm so glad it helped, Henry!! :D
That's how I thought of it too. I think with most high school math, you don't really need to 'understand' the topic to ace it or do well on a test but with higher and higher level math. It's a lot more conceptual and 'hypothetical' even that remembering how to do a problem just wouldn't cut it more.
Guys at 10:43, the average velocity is change in position over change in time. Krista made a little error, we are all human :)
yep i had noticed the same thing
Is the average acceleration then change in velocity over time?
THANK YOU I was so confused
For calculating Average Velocity, shouldn't you use change in position over the change in time rather than the change in velocity over change in time??
Who else is barely starting to study for the test..... no one... just me? Lit
Yup living the dream 😞
My dude the test is in six hours and I'm just now starting
SemiSolid Snake same
@@tylershep4220 how did it go
@@cubingpro9877 I think I got a 3 lmao
This video was so helpful for me because I literally felt unprepared for my ap calc exam tomorrow but after watching this I feel more ready. Thanks a lot appreciate it
Everyone says calculus is tough , even related rates problem. But I to be frank felt it is super easy ☺️☺️☺️
That’s great !
omg, thank you so much for this video! you are saving both my life and my grade
i’m watching this the day before my ap calc test
Error at 16:49 when calculating derivative of a=1/2bh. you need to use product rule!
You're incredible. I am in awe of your skills.
Amazing video, thanks for the help!!
That was great it helped a lot since the classes hurried this chapter and i don't know why but after learning from you i also want to teach maths 😁
Thank you so much for making these videos! They have been very helpful :)
This is amazing and well explained I am following you Krista. Queen of Calculus
Wow I used to watch your videos years ago for help in my math classes! Truly, thank you so much for continuously providing help to so many people for over a decade. I hope you know how many lives you help out across the world ❤
There is a mistake in this video around 11:19 when calculating average velocity and average acceleration. What is actually computed is the average acceleration and average jerk (rate of change of acceleration). The antiderivative of a function is used to calculate its average, not the function itself (unless it is a linear function in which case it can be computed with the [final value plus initial value] divided by 2, not the width of the interval).
thank you for the dense but easy to understand summaries. super helpful
You're very welcome, Strollas! :)
I learned that velocity average would actually be solved by solving for the change in position over time not change in velocity?
Thanks so much for your great video and I really need it to teach my little brother. However, there is an error when you talk about the average velocity and average acceleration. The formula for Vavg you used is actually for Aavg. Is that right?
BTW, I was have a question. When you take the derivative of the pythagorean theorem, can't you cancel out the 2s or do they need to be included when calculating the related rates?
they have to
Thank god I’m no longer taking calculus. I passed and never have to worry about it again.
Do you suggest buying the ultimate review packet near the end of the year (closer to the exam to fill it out at once) or right now?
Hey, hope! If I'm in your shoes, I'd do it now. That way you can use each chapter's review packet when you're studying that specific chapter in class, which will help you solidify that chapter better at the time. Then you can do a final re-review at the end of the year before the exam. I think it works best that way! :)
Thanks for the great video!
My pleasure, Clay, glad you liked it! :D
Very helpful
Amazing!
I had a question. At 12:30 you said that average velocity is measured is m/s and and average acceleration is measured by m/s^2. So why did you plug in 9 and 0 into the v(t) function to find average velocity. Shouldn't you have used the X(t) function instead? Isn't average velocity the same thing as average slope?
Yeah, she should have been using position formulas to calculate the average velocity, and v(t) to calculate average acceleration.
yeah you are right
Same thought. Tripped me up for second but then I was like… if acceleration is just 6m/s^2 how can the average acceleration be zero?
Awesome!! Thank you so much ma'am! 🙏
You're welcome, Hemung, I'm so glad it helped!! :D
At 10:17, why the average velocity is not = [x(9)-x(0)]/[9-0] ?
@MOHAMMED FADEL when she says avg velocity or avg acc, what she actually means is the rate of change. so if the acceleration is 6 throughout the whole graph, the avg rate of change of the acceleration is 0 since its a horizontal line.
great explaining!
Thanks, Anoushka, I'm so glad you liked it! :D
With L’hopitals rule, what happens when u substitute and the denominator is 0 but the numerator is not, could u still use L’hopitals rule?
No
This is very good, from an engineer's perspective. Good job
Exactly!
Thank you so much, Erik!
Can you please put up units 6-8 for calc ab? Thank you
please 🥺🥺🥺
Can you make videos for Units 6,7,8? Thank you so much for the videos you've made so far!!
hello! I just wanted to say it would be so incredibly helpful if she would make videos for units 6, 7, and 8!
@@iamyourfathernamjoon7202 she did, but they are paid on her website
Thank you so much
You're welcome, Iyad! :)
Soo helpful
Oh good! I'm so glad it helped! :)
When you say average velocity or average acceleration, that means average rate of change, correct?
Yes, average rate of change of velocity and average rate of change of acceleration. :)
@@kristakingmath Should the unit of average rate of change of velocity be m/s/s? And the unit of average rate of change of acceleration be m/s/s/s? Thank you for everything!
@@ayandas8299 Yes, either she messed up the units and meant to do rate of change of velocity and rate of change of acceleration, or what I think is more likely is that she meant for it to just be average velocity and average acceleration and just used the wrong formulas
test tommorow ;;;;)
The problem w related rates is there really arent many of them on the AP exam lately, so spending a lot of time on them is not valuable..
its 3am , i thought this would put to sleep , but its intresting
Lol, love it! Maybe try ASMR next time for sleep? 🤓
Anyone else watching these the day before AP Calc BC tmr lol
yes me hahaha.... :(
it's literally in 8 hours and i just started studying
@@dylaancaarpio 2 times speed easy
Today we can build Electronics Circuits implementing these mathematical concepts into analog and digital electronics, Electrical engineering and software for 'artificial intelligence' computations for Controlling anything in the Physical World? ...
Great video, thank you 😍
You’re welcome, joanna! 😊
Oh yeah
13:05
Wait a second. Will you upload all of your "premium" videos that are available in "The Ultimate Review Packet"? I thought the first ones here on RUclips were just teasers 🤔
Hey, Kelvin! The Ultimate Review Packet is all about interacting with the videos to make sure you really understand the concepts and can apply them! That's why the study guides and practice questions, plus full solutions and explanations, are the most critical part. Plus I've included full AP practice exams, which are a huge help if you're getting ready for the AP test. :)
You saved me. Because of you I passed my midterm and the semester. 😩
I'm so glad I was able to help! Congratulations on passing the midterm and making it through the semester, that's awesome! :D
Your voice is so sweet!
Hi
17:00
No
Daddy God bless you.
u made a mistake in calculation the average accleration
Yes, you are right. At 11:35, I realized she found the avg acceleration when she said she was finding the avg vel. If v(t) = 6t + 6, then the slope of vel = 6 which is always the acceleration (which of course is confirmed when says a(t) = 6. But most everything else Krista does is great, so I am still recommending her videos for my AP Calculus AB and BC classes as review.
You're not only a beautiful woman but also a great teacher, thanks.
Creep.
Marry me, I am just 18 but by watching your videos I will be great mathematician one day, and earn lots of money. I will love you and care about you. Marry me, accept my proposal, when I will grow up, I will come to propose you.