Calculus 1 Lecture 2.4: Applications of the Derivative

Max height will be when you plug in 8 for t, in s(t)

Uh-oh, capitalism calculus.

i wish i had met with these videos 2 years ago, btw THANK YOU VERY MUCH SIR FOR YOUR EFFORT

After watching multiple videos on applications of derivatives, I only found this one good. Thankyou for making it. And I must say that you are a handsome professor. ☺️

What's a dvd lol

He looks like Senator Armstrong from Metal gear

Thank you for not being indian

Dear Professor Leonard (and any other boffin who may see this ;) )
P.S. Prof: I'm sorry about spamming these on your videos. I'm just in desperate need of help. I understand if you can't provide it personally - you seemingly have a lot on your plate as is! However, I am hopeful that at least somebody knows how to get around this.

I am studying a Calculus I course at my university, but the work is wayyy more rigorous than how it is laid out in the textbook, or even how it is on the internet. Professor Leonard has helped me a lot in getting me to understand the basics and my marks have gone up by 5-10% ever since. But I still can't understand some concepts in the calculus context. (ie. Triangle inequality, bijection, invertible, and many others). For a better idea of what I am complaining about, here is a OneDrive link with my previous homework assignments: @t

Thank you so much for anyone who may help me! Also, thank you to Professor Leonard for giving the motivation and confidence to see that I can get around this huge obstacle. I may not be around it yet, but you have at least given me the confidence and have picked me up when I was down

How are these functions created in real life, is there a branch of mathematics that assigns formulas to real world problems so these techniques can be applied? Some mathematical modeling field or something. I have seen formulas derived theoretically in physics, but how are these math functions assigned in real life? Otherwise, calculus is just sitting in as mathematical sophistication with any proper useage right?

Simply the best

cool fuckin vid. mvto

I have a exam on jan 12.. My teachers methods are too complicated. 2 mins into ur video and its really different.. Thank you for this and ill update after my test.. :)

Hi! Could you please turn on auto subtitle? Because English is not my native language , the sub. help me so much. Thanks for videos!

ofc im here because i need to study , not to see his arms

I wish i had a teacher this good

Some teachers can't articulate these things clearly. YOU can! Thank you!

Like how do we know that this is the equation of the scenario how we came up with it sir @leonerd

OMG I loved the way you're teaching (and of yours muscles lol)! Thankssss♥

Thanks very much for the video. So in the question of DVD sales, the peak happens at t = 1 year and if I substitute t = 1 in S(t) that would amount to peak sales of 3.5mn (Say) in year 1. But at t = 0, we find that the rate of sales would be 7m/T by setting S'(t) = 0. My understanding is that the highest rate of sales would probably be at t=0, and this rate decelerates as T approaches 1 where it becomes zero. When we say it peaks at T=1 year, we mean that the cumulative sales from t = 0 to t= 1 is 3.5m and bulk of the sales happened in the early part of the year and slowly decelerated to the end of year. I can understand that the 7m/T rate at t = 0 but unable to visualize the meaning. Does it mean that at the point of launch t=0, and if the same rate of 7m/T continued till the end of year 1, we would have sold 7m instead of 3.5m. The 3.5m figure is because the rate of sales decelerated and that kind of makes sense. So the next question is, if some one asks me what was the sale at launch - how can I get that number ? I have the rate of change at t=0, but how to arrive at the number of copies sold at t=0. Thanks very much in advance !!

For physics geeks like me it's very interesting that he discusses the third derivative of position as a function of time: jerk or the change in acceleration. Most people only experience that when you begin accelerating in a car or stop suddenly or on an amusement ride. Constant jerk like in the example he gives would be experienced on a spinning ride where you feel yourself being pressed deeper and deeper into your seat as the speed at which it spins increases assuming the speed increases uniformly. (in a spinning ride you are accelerating even when the rotational speed is constant so an increase in rotational speed is a change in acceleration and therefore jerk (you don't have to feel "jerked around". )If you listen to the cockpit transmissions of the Apollo 17 launch, commander Gene Cernan describes the build up in g forces as the saturn V's acceleration increases. This is also an example of jerk.

I hate application problems they're hard for me to understand but you have done an awesome way at explaining them clearly. I get it now. thank you

i wish i watched this series instead of wasting my time trying to learn in collage

gawddd, dvd sales. Does anyone still buy those?

Doesn't derivative collect basis house or mall.

real life Clark Kent helping us out weather it is math or cost of doing bussiness

So I can understand when the slope change sign from positive to negative, we should have a peak. But I think it doesn't guarantee at that point the slope will be 0, it that peak is a sharp point, does it count as a peak? Graph like this: /\

Thank you professor

Excuse me sir, how did you get the DVD sales which is= S(0)=7?

Excuse me sir, how did you get the DVD sales which is= S(0)=7?

Excuse me sir, how did you get the DVD sales which is= S(0)=7?

10 years later, wonder if he’s getting those DVDs

I'm watching this video in 2024

What would a negative marginal cost (i.e. C'(x)<0) mean? That you're making money by producing an item? At what point does this formula stop representing the real world?

😮 Fascinating Lecture ... 🧮 🤔💭

😬📝 I love taking ... Duh - rivatives. 🤭

Thank you

Best calc teacher ever

Which secotions of Stewart 's Calculus Early Transcendentals 9th edition do I have to work out related to this lecture?

2025, 2:47am Sunday May 25th