Finals in an hour, and I'm here from the related rates video

@trombonetimmy1064

Жыл бұрын

Sigma dressed tight watching PDE before the final

@Evan-lq3wt

7 ай бұрын

History repeats itself

@Hulett91

7 ай бұрын

@@Evan-lq3wtexactly the same 💀

@user-be9pk8my6x

3 ай бұрын

watching this while driving to take my IB math exam

I like your channel so much. You explain everything in the best and the easiest as well as in an interesting way. Thanks Professor Dave. Make more videos.

Optimisation problems is arguably the best real-life application of calculus

@chris2217

Жыл бұрын

related rates

@Alex-ns6hj

3 ай бұрын

@@chris2217I feel like diff eq is more useful for that though…

I have been struggling in ib math and this helped me clear up what my teacher taught for the past week. I watched your videos for chemistry, physics, and now math. You have saved my life sir. 🙏

@hydromic2518

Ай бұрын

I’m doing IB too and Prof. Dave is 🙏

You are seriously the best. Thank you so much for these videos.

I FINISHED DIFFERENTIATION LAST YEAR BUT UR VIDEOS HELPED ME MASTER IT DAVE THANKS!

Every time I hear your intro song, my thoughts turn happy and I know that this difficult subject will soon be understandable. Thanks Professor Dave :)

Another very helpful video! Thanks Professor Dave :)

man your videos are helping me pass finals in computer science ! thank you mate keep going

This is exactly why people like me are actually asking for when we ask what this has to do with anything or what will I actually use this for. Our minds work backwards. If you tell me the rule first, then the application, I forgot the rule because it had no relationship to anything I understand. By showing the application and what the variables relate to, it's so much easier to remember the rules or learn them while applying them. I wish all math videos would explain according to this concept like this video. There are already too many that do things the other way.

@eldersprig

5 жыл бұрын

Look em in the eye and say scheduling major league baseball. OK. not calculus, but more advanced stuff.

@ThueringerNeuland

5 жыл бұрын

I felt like this too, but it gets better over time. I guess I developed some kind of „trust“ in maths, to be useful in the real world. :D

@Backflipmarine

5 жыл бұрын

I like how you put it, "our minds work backwards". true.

@ericfricke4512

4 жыл бұрын

Instead of saying "our minds work backwards," you can say you prefer a "top-down approach."

Thank you very much mathematics is always simple with professor Dave.

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

Dave! Your videos are incredible, I was quite stuck on Optimization/Related-Rates using derivatives, but you've cleared it up almost effortlessly! Great professor, truly, lol. Thanks again!

Instead of watching the useless online lecture videos my professor posts, I come straight here to get edumacated

Thanks for changing my views on calculus!

Thanks for the video Professor Dave. Brilliant explanation.

Dude... Your a true god. Love your vids :D

Thanks, Professor Dave..

sir your tutorials are very helpful

thank u for this !!

Thank you!

really interesting. I thought the area should be maximized when simply having the shape of a square. The farmer example shows DO THE MATHs

✨Thank you, Sir, 🙏🌺✨for all of yours beautiful videos🙏🏼🌺✨Please keeping teaching us🙏🏼🌺✨

thank you for so awesome videos

Thanks professor dave😊😊😊

Math is like my bff for life because I'll use it to create a new cure for cancer when I'm a chemical engineer

@tanvirfarhan5585

3 жыл бұрын

@@brettandy9718 it wants money

@natidaschoolboy

15 күн бұрын

It's been 4 years, how is that going?

Thank you very much I understood this lesson so fast it helped me a lot

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

optimization is by far the hardest topic in calculus 1, it was going well until then

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

@yaowang9883

2 жыл бұрын

me too

@soccerbels7947

2 жыл бұрын

Even harder than calculus 2 i think

Thanks, Prof!

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html

AMAZIN VIDEO

you're so good at teaching calculus may God bless you Sir❤

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

@professor dave sir....for the same question how can I find both maximum and minimum values...suppose I have 2400 m fence...how can I find the minimum area...pls explain it sir??

@carultch

Жыл бұрын

In this problem, the minimum area occurs in the degenerate case that you make the plot of land either infinitesimally thin or infinitesimally narrow. The corresponding area would be zero.

At 7:22 how do you get the common denominator r^2?

I'd always wondered how the solver function on Excel worked, didn't know it was something I could actually do by hand lol.

preparing for my calc test today

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

Wow what a nice video 👌

POV: You have a test in an hour and can't remember anything.

if extrema is not the highest or lowest point of a function. Then why they are the most optimized?

if only the farmer knew his farm would be bigger if it were a half circle

Just wow

Mr Dave Rave. you helped me get into Uni, and now helping me go through it (biochem). Ive always been known as the "not the sharpest tool in the shed" girl, cause i really am and there is no shame in that so thats a testament to your amazing italian teaching skills that im finally learning. I got into one of the best unis here with your help. Maybe late started (24). but still. I cant even speak my native language well cause i have trouble with language cause i hit my head really hard when i was young. (no joke, but you are allowed to laugh), but hey this is an achievment for me, so let me be happy. thank you very much Mr David, and thanks to Italy for bringing great things. like you, the godfather and pisa (the tower not the food)...no but really. Thanks sir, and cheers from Chile! youve helped me a lot!

Thank you for this serier.. But i have a doubt. if rather than covering the max area we have to cover the minimum area with same fence. Then how would we solve this ??? Thanks in advance.

@lucyla9947

7 ай бұрын

8 months late, but essentially what he's doing here is calculating a Maxima, to calculate the smallest area you would need to calculate the Minima, which is done practically the same way. Both Maxima and Minima have a derivative equal to 0, you just need to check which one your equation gave you.

Dear professor,may l ask you a question, is optimisation calculus a part or an exception of infinitésimal calculus ?

@carultch

2 жыл бұрын

Calculus used to be a generic term for calculations in general (obsolete meaning of the term), with infinitesimal calculus being what we call calculus today. The way the term calculus is used today in mathematics, it is all infinitesimal calculus. There are two separate branches of calculus, which are integral calculus and differential calculus, both of which are related through the fundamental theorem of calculus. It means something completely different in dentistry, but that is the only meaning of the word that is unrelated to the way the word is used in mathematics.

'tis was v informative

@astronm64

3 ай бұрын

Or maybe it was dx/dt informative?

For the fence problem, I did it differently. I said dA/dx=y and dA/dy=x. Upon reaching this calculation, I intuitively thought, "no matter which variable we choose to differentiate A(meaning no matter how we try to find the rate of change of A with respect to either variable), they must be equal to one another ". That being the case, I said x=y. From there, I said 2x+x=2400(since y=x).

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

@christianherrera4729

9 ай бұрын

Maximizing the area doesn't mean making a square like you have. For this problem we have 2x+y = 2400. Solving for x you will get (2400 - y)/(2) and solving for y you will get 2400 - 2x. Their derivatives will be different, and solving for x will get you 600 and solving for y will get you 1200. What you're doing doesn't really make sense.

Hey prof, can the second derivative be 0, if so would that mean the second derivative test failed?

@megerbig

3 жыл бұрын

The second derivative can be zero, and that means we can't use the second derivative test to find the local min/max for that point.

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍

in the first problem, if the sides are for example 605m x 1195m = 722,975. I get a much higher area, why?

@user-hv6ef9ie1g

2 ай бұрын

Because 605+605+1195=2405, even though we only have 2400m of fence to use. You got a much higher area simply because you have 2405m of fence, not 2400 (like the problem does).

How would you know to do 2x+y=2400m instead of x+2y=2400m?

@carultch

2 жыл бұрын

In this problem, he's defining x to be the vertical side. Since there are two vertical sides and one horizontal side, we need to use 2*x + y = 2400 m, rather than the other way around. He could've just as easily assigned x to be the horizontal side length and y to be the vertical side length. It was an arbitrary choice.

What this guy taught me in 10 mins is what my teacher failed to teach me this week

Dancing to "checking comprehension" music when my answer is right

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

@ygreaterr

3 жыл бұрын

@@beoptimistic5853 ok

If for both Max and min you set the derivative to zero, how do you know if you’re getting the max or min?

@ProfessorDaveExplains

3 жыл бұрын

2nd derivative test! Or sometimes it'll just be obvious.

@christianherrera4729

9 ай бұрын

If you have a quadratic, just look at the sign. + means you have a min and - means you have a max.

What should we do if we want to find the maximum,but then do the second derivative test and find out that we are actually finding the minimum?

@carultch

2 жыл бұрын

Then you investigate the end-points of the domain. One of those will be the maximum. As an example. Two positive integers have a product of 100. What is the maximum possible sum? You'll find a critical point at x=10 and y=10, where the sum is 20. This is a local minimum to solving this problem with calculus. We were interested in a maximum, rather than a minimum. But 5 and 20 are another pair of integers whose product is 100, and they add up to 25, which is greater than 20. To get the maximum sum, we have to look at the end of the domain. The smallest positive integer is of course 1, and the corresponding other number in our constraint is 100 itself. 1*100 = 100, and 1+100 = 101. This is our maximum.

wallah you re the best habibii

What if you only get one fixed solution to the derivative.. then how would you determine whether it's maximum or minimum

@carultch

2 жыл бұрын

The second derivative test. Or more generally, the even order derivative test. If the second derivative is negative, it is a local maximum, with concave-down (negative) curvature. If the second derivative is positive, it is a local minimum, with concave-up (positive) curvature. A second derivative of zero, is inconclusive. You have to continue taking derivatives until you get to an even-ordered derivative that is non-zero. A forth derivative can conclude the same thing, given a second derivative of zero. If all even-ordered derivatives are zero, then you have an inflection point that coincides with a flat point on the graph, like you see for y=x^3. An inflection point is a location where the curvature switches from being concave-up to concave-down, or vice-versa.

Wait! I think I understand now. Derivative is actually the SLOPE OF TANGENT LINE of a function. So when it's 0. That means the tangent line is going horizontally. This means that the function's y value can't be any greater as it is contained by the tangent line. Thus the f(x) is largest when dy/dx =0. Am I babbling??

The part of Calculus that actually might be useful to my life.

In the first example using 2400m of fencing the constraint was that the enclosure was to be rectangular with one side being the river, but what if instead of a rectangle the fence was arranged as half a circle with the river being equal to the diameter. In this case the area enclose would be over 916,000m --nearly 200K more than the rectangle. One of the problems with questions like this is knowing what the constraints are and in this case the constraint was clearly stated that the enclosure was to be rectangular, but what if that constraint was not specified and the question was: what would be the greatest area enclosed with 2400m of fencing if some portion of the enclosure was defined by the river. How do you determine the ultimate geometry to use?

@ProfessorDaveExplains

5 жыл бұрын

Hmm, I guess you just try different shapes and see what happens! I'm pretty sure a semi-circle will maximize the area though.

@Raptorman0909

5 жыл бұрын

@@ProfessorDaveExplains -- Well it makes sense that a semi-circle would be pretty good as a circle is known to have the greatest area for a given circumference or perimeter. I guess my question or point though is that in some max/min cases the geometry or constraint is not well known so narrowing down or pinching the constraint is a bigger problem than the Algebra or Calculus. BTW, thanks for doing these videos -- its been a long time since I studied these topics (mid 80's) so its nice to refresh my somewhat atrophied brain cells.

@carultch

2 жыл бұрын

@@Raptorman0909 A circle has the optimal area-to-perimeter optimization, but that is only if we are interested in the entire perimeter. In this problem, one given side is the linear shore of the river, and the shore of the river is "free fencing" for this problem. We may be able to do better than a semicircle for how to optimize shape of the fence. I've attempted this using Ramanujan's approximation for perimeter of an ellipse, and surprise/surprise, a perfect semicircle is the optimal semi-ellipse for this problem. There could be a shape other than an ellipse, that optimizes the area of this fence.

thank god

Your work is terrific but still need more in detail, if it’s possible please

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

thankyou lord calculus

Done.

thanks

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍

why is it that when x is positive, it is the local minima and when x is negative it the local maxima?

@carultch

2 жыл бұрын

Whether x is positive or negative, has nothing to do with whether the point is a local maximum or minimum. The value of x just indicates what the horizontal position of the point is, representing the input of a function. It is the second derivative d^2y/dx^2 that determines whether the point is local maximum or local minimum. And the reason is that the second derivative indicates the curvature of the function, and the sign of it indicates whether it is concave-up or concave-down. A positive second derivative indicates concave-up, and a negative second derivative indicates concave-down. A local maximum should slope down away from the maximum point, thus being concave-down, and vice-versa for a local minimum.

While differentiating the area, with respect to what we are differentiating? Help me with this.

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

@carultch

2 жыл бұрын

The area is being differentiated relative to the independent dimension that is to be determined. He's looking at the land area as a function of the x-dimension perpendicular to the river.

10:17 where did the A=xy came from?

@astronm64

3 ай бұрын

A represents the product, so the multiplications of two integers (x and y) equals the product (or A)

@user-hv6ef9ie1g

3 ай бұрын

@@astronm64 Ohh, i see. Thanks

Dear sir, how can i concrete Sketching derivatives function on the graph, i feel that i still need some more, will you do some other videos about this?

@ProfessorDaveExplains

5 жыл бұрын

i have a tutorial on graphing functions and their derivatives! check it out.

shen gennacvale dave

Make more videos to co-realte with theory.

I laughed so hard at 8:49 for some reason 😂

Dave - you have created disharmony in my head. For 50 years now I have been under the impression that the common tuna fish can was optimized for materials. I can remember sitting in my calculus class in junior college and being amazed by the proof of this from the instructor. I watched this video of yours and realized that these optimal dimensions (h=2r) don't match with a tuna can in my cupboard. I measured it, and h=r approx. What the heck ? Did I misunderstand my teacher all those years ago, or is a tuna can not optimized ?

@christianherrera4729

9 ай бұрын

There is actually a lot more that goes into designing a tuna can. I saw a tweet about it a long time ago, but someone was trying to tell a cat food manufacturer that they could save money by optimizing the surface area and whatever. One of their engineers replied and basically said there are like 10 other factors that go into the cost of manufacturing that all outweigh this optimization.

did he knew ahead of time that x = 600 is a maximum point, what if it's a minimum or not an extremum point at all, what I know is we must check at first using the first derivative test or use second derivative to check for concavity instead.

@carultch

2 жыл бұрын

By intuition, you probably can tell that it would be a maximum point, rather than a minimum point. You know that for a full rectangle, the optimal solution for area to perimeter ratio occurs when the rectangle is a square. So a very long and narrow rectangle, or very wide and short rectangle, are likely not the answer. You know that a solution with maximum area would be somewhere in between. And since this is a continuous and differentiable function in the entire domain, you know that the only critical point you find, will correspond to the maximum. You can do the second derivative test to confirm it is a local maximum, and after ruling out all other critical points, and end points, you can confirm that it is a maximum.

My maths teacher taught me a great rule about this that can help you instantly figure out how much this was when for example have x+y=100 the maximum product of this two numbers will be 100 divided by 2 and this works every time.

@giorgibregvadze49er

2 жыл бұрын

As it did in x+y=400

👍

I wrote it.

The funny thing is i solved comp. without calculus so lol

neat

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐

He doesn't Explain why area would be maximum when the derivative of the function is 0. Does he understand why? Coz I don't know either. AND I DIDN'T SAY ONE PEOPLE ASK WHY DERIVATIVE OF A FUCNTION IS 0 WHEN IT'S MAXIUM VALUE

@hydromic2518

Ай бұрын

It’s 0 because it means the functions slope has stopped increasing, the tangent line at that point would be a flat line meaning the function must decrease afterwards.

8:35 Not true. f(x) = x^3 at x = 0

@ProfessorDaveExplains

4 жыл бұрын

Huh?

@DarinBrownSJDCMath

4 жыл бұрын

@@ProfessorDaveExplains It's not true that "when the derivative of a function is zero, there is a maximum or minimum at that point." I think you meant to say the converse, which is true provided the derivative exists.

@ProfessorDaveExplains

4 жыл бұрын

I don't understand what you're saying. You cited x^3 at x = 0, where the derivative of the function is not zero. That's why there is not a local maximum or minimum there. I am not aware of any example where a derivative of zero does not indicate a local maximum or minimum other than a constant function.

@DarinBrownSJDCMath

4 жыл бұрын

@@ProfessorDaveExplains The derivative of f(x) = x^3 is f'(x) = 3x^2, and f'(0) = 0. It's a stationary point, but not a local max/min.

@ProfessorDaveExplains

4 жыл бұрын

Shoot, I guess that's true. But is it an inflection point? When the derivative is zero there has to be some special behavior, no?

Will you do intergration (Calculus II)

@ProfessorDaveExplains

6 жыл бұрын

Yep! Starts next week!

@Thaumius

6 жыл бұрын

cool!

Thank you Science Jesus !!

200,200

Thank you Jesus

This is the first time I can't understand

:)

math jesus

👍

@beoptimistic5853

3 жыл бұрын

kzread.info/dash/bejne/ioR3yamNaaXSorQ.html 👍💐💐💐