AP Calculus AB and BC Unit 4 Review [Contextual Applications of Differentiation]

► My AP Calculus AB and BC Ultimate Review Packets:

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.

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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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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?!”

[kristakingmath]

Who's ready for RELATED RATES?!! 🙃

[quinnwalker]

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.

[rushabhshah]

These videos are very useful for someone trying to refresh their memory a few days before the test. Much appreciated.

[jamestrujillo]

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👑 👍👋

[hemungkapoor]

One of the best teachers I've ever seen for mathematics

[lyndonyang]

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??

[Hamza_Khan_Journey]

Guys at 10:43, the average velocity is change in position over change in time. Krista made a little error, we are all human :)

[strive]

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

[manishkota]

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?

[strollas]

thank you for the dense but easy to understand summaries. super helpful

[yabesira]

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?

[cristianmendoza]

Who else is barely starting to study for the no one... just me? Lit

[elizabethknightly]

i’m watching this the day before my ap calc test

[dougmcnally]

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).

[anishvijaybhatia]

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?

[fmbm]

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 ❤

[cornopeanus]

You're incredible. I am in awe of your skills.

[DingoDummy]

omg, thank you so much for this video! you are saving both my life and my grade

[zhaoyiming]

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?

[yasekins]

I learned that velocity average would actually be solved by solving for the change in position over time not change in velocity?