Awesome! Now do sum of reciprocal cubes.

Thanks it helped a lot

super amazing video

This a perfect video! Thank you very much!

What about f(x)= x^2, if x < 0 0, if x ≥ 0? It has an inflection point at x = 0 according to your definition. Did you intend this? You didn't show functions like this in your video.

Thanks so much!

Hello Chris...at 18:08 , is it sufficient to conclude that if f is defined on an interval then accumulation function of f is an anti-derivative of f ? But for instance, if signum function is defined on an interval [-1, 1] then accumulation function is not an anti-derivative of signum function as accumulation function here is not differentiable on (-1, 1).

Bravo!

Polar coordinates are hard to understand and this video was simple to learn the basics. @8:37 when the arctan(2/5) is 0.381 which lies in the range of inverse tan i.e -pi/2 to pi/2 why would we have to go back and add pi to that.

Probably it's a good explanation

3:00 This formulation method is a genius. I salute you, brother.

ok so just do it with a given area A, or I suppose conversely a volume V

Thanks so much for this video! Do you happen to know which definition for inflection point is used by the College Board for the questions on the AP Calculus exams? I looked in the AP Calculus Course and Exam Description and it didn't seem to say explicitly.

This is the simplest to understand. I love this🎉❤

255 degrees should be 4pi/3 radians on your unit circle 1:13

how do you make your presentations

Awesome

The aluminum on the tops and bottoms of soda cans are twice as thick as the sides. If you change your equation so that the surface area =(4*Pi*R^2)+(2*R*H) to represent using twice the aluminum on the tops and bottoms, then you'll get the right answer. The radius (cube root of 355/4pi) is 3.046 cm, making the height 12.18. Much closer to the 2.7cm - 3.3cm range for the radius and 12.3cm height.

Thanks ..the best and the more explicit video on how Euler did resolve this problem...you are awesome Odden

Very helpful thank you sir

Very helpful, thank you.

Absolute chad video I will get an A in physics 2 literally because I can do this stuff in excel now thank you king

Best approach ever seen ! Nice job.

this is a great explanation. super simple, useful and not too technical

And we can generalize it for all positive and even arguments of zeta

Now an introduction to polar bear coordinates. Wherever there's a polar bear, my butt is vectoring with great magnitude pi radians relative to it.

If we take open interval (a,b) what will be the problem

I don’t understand why you didn’t just take the integral?

Excellent explanation and visuals. I find myself lost in the text definitions constantly. Supplementing and having a way to visualize what is being stated is integral to my understanding. I appreciate your work 🙏🏻

A little late to the party but consider making a cost function using the surface area (i.e. the aluminum costs some value per square cm). If every part of the can costs the same amount nothing changes (besides maybe a scalar). However, it seems reasonable that the top and bottom material would want to be thicker and say, twice as expensive. This new cost function actually does optimize to something very close to a standard soda can (and of course companies want to optimize cost!).

Thank you very much. Just what I needed to know. These proofs evoke a peculiar and wholesome inner ecstasy. (enstasy ?)

OMG THIS IS SO COOL AND GOOD!

doesnt scalar multiple rule contradict product rule?

why is double derivative positive for concave upwards?

Very helpful 👍🏼 and we'll explained

why did you particularly use the cubic function and not choose the quadratic function that forms the area that is rotated?

Awesome explanation, thanksss for sharing. Could you tell the tool which u use to prepare the graphical representations?

Thank you so much sir! This helped a lot :)

Great videos, they will be handy next time I teach calc 1 or 2. Thank you for making them! Also, do you mind sharing what you used to make your slides and animations?

you're an amazing teacher. I learnt a heap from this video.

Amazing video!

ok, subscribed.

Umm.... your endpoint conjecture is absolutely wrong. If end-points are included in the domain of the function and they have a defined value, then they should absolutely be considered for possible global extrema. If an endpoint value is higher (or lower) than all other values, why wouldn't it be a global extrema? Endpoints cannot be relative extrema (by definition), but global extrema may occur at relative extrema and defined end-points. If you do not check defined endpoints for global extrema on any AP Calculus exam or any Calculus entrance exam for any college/university, you will get the problem wrong.

introducing the r/h ration would lead to the same result much easier... in regards of why manufacturer do not follow this rule, it is not only it looks "bigger", but it also the dimater an avarage hand can hold... it would take just some educative facebook campaig to explain that actually the best shape is when the 2r/h ratio is equal to 1...it could save million tons of wasted material

This is awesome, you are the calculus god. I will worship you and start a new calculus religion 😅

Best video ive seen on this topic!! could you make one on interpolation??

Hi Chris... I have seen about 10 videos on this Law of Cooling... and there were some very good ones.. BUT... Your Video here is the BEST by far!! Thank you for your complete Presentation of all aspects of this Topic.. Amazing!! I am a Subscriber!!

Your videos are criminally underrated

Hi, I have a question regarding the first derivative test and second derivative test. Using the first derivative test and finding critical numbers, testing numbers either side of critical numbers I can determine if function is increasing or decreasing because slope is negative or positive, therefore the critical number itself I can intuitively determine is a relative max or min depending on the test values and where they increase/decrease either side. The second derivative test, find the critical numbers of f’(x), find f”(x) and substitute c.n’s of f’(x) into f”(x), if f”(x) > 0 then minima and same shit/vice versa for maxima if < 0… So if I can determine relative max/min using first or second derivative test, why even use the second? Is it just a preference thing.. ? Some people might like to substitute the value in and know directly… where other people have to use test values / sign diagram for the first derivative test.. but either way.. they give same result don’t they?.. That is what I need clarification on.. They give same RESULT don’t they ??