Thank you, professor Jesus.

@jacobkouteda9501

3 жыл бұрын

Hah professor jesus😊😊

@crooner6255

3 жыл бұрын

😂😂

@charlesokoh3373

3 жыл бұрын

even after he started with “it’s professor Dave...” 🤧

@qualcomsaga8508

3 жыл бұрын

He looks like so!

@ujaanroy3075

3 жыл бұрын

You know what they say, "God is always there for you even when your math teacher sucks"

He says "that one was pretty simple" just as my brain was about to explode.

@drumpfbad5258

4 жыл бұрын

Are you in AP calc?

@mariakhan6090

4 жыл бұрын

It's very simple for us Asians 🤷

@RedEyedJedi

4 жыл бұрын

​@@mariakhan6090 I'm part Asian too but I'm mainly English. If I pointed out I find programming easy, purely because I am English, people would think that was racist.

@photocide17

4 жыл бұрын

It was literally the easiest.

@froopi2

3 жыл бұрын

Noob

Sir 'Professor Dave Explains', i just wanna let you know how grateful and lucky i am. watching your calculus video is enlightening. i am from philippines, currently out of school. i am doing some review on my math subjects before re-enrolling again. i am also a self learner, and thanks to you because i am on a great progress with calculus (self taught). i never learned it from the school, i learned it on your calculus videos and some old books. you saved me. im hoping that someday, if i happen to meet you in person, i have already achieved my dream of becoming a good mathematics teacher. Thank you so much sir.

@ProfessorDaveExplains

5 жыл бұрын

good luck!

@kumaransrinivasan2639

4 жыл бұрын

it is very good exblain

@kumaransrinivasan2639

4 жыл бұрын

🌎💎👍

@jgja1931

2 жыл бұрын

From Philippines too❤️

@julianpaulo6817

4 ай бұрын

nice one pre!

this man is indeed a true knowledgeable person.....knows how to apply his learnings practically......his videos should have more views but unfortunately people dont care to learn things in such detail.....but people like me are a fan of his videos.....lots of love and respect professor dave..... moreover people don't realise a crucial thing if learning can be put practically there will be no need of tedious practicing......maths would become fun....thanks dave....i am not financially that strong to support your channel....but someday i will...thanks please continue making such videos on valuable topics

@egggames8059

8 ай бұрын

U like ellipses perchance?

Your great at what you do man! The reason these specialized videos don’t get many views is because only a select few need this type of information and your competing with khan academy etc. As more time goes on these type of specialized videos will have so many views and help so many people. I’ve already seen you covering more broad topics and they have a ton of views and are structured excellently for learning. I come to your videos for all my topics your amazing!!

@ProfessorDaveExplains

6 жыл бұрын

woohoo thanks! yes i think that once i am finished with calculus i will find a way to advertise a little bit and then it will get a more appropriate viewership. but thanks for watching and spread the word!

@robertbocklage1249

4 жыл бұрын

@@ogstephh shut up idiot

thank you Professor Dave! I learn math on my own and your videos make my life easier and more fun.

Thanks I was struggling with this ..from quite a long time and finally got it. Thanks once again.

You just make my work easy .. Thank you so much from South Africa ❤

thanks man, 2020 put me in online and instead of reading the notes they give us imma just look up videos on how, thank you

Thank you Mr. Professor Dave, I would like to thank you for explaining this concept. Now I understand local maximum and minimum. May God Bless You and His Peace Be Upon Upon Always!

how to find the maxima and minima of a damping signal as it has more than 1 point with m=0?

Professor Dave is the best.

a great source of required information.....Thank you sir...

Thank you so much sir.. this was too useful and helped me a lot..

You had explained the whole concept in clear and precise way.... Very fantastic teacher u are

Professor Dave is daddy. Literally has gotten me through physics and calc this year.

Hi Prof, @3.07 by looking the graph i can say local min & max are -2,+2 but the solution you have is 0,2. Im bit confused

Fantastic explanation sir

Keep on enlightening inchoate mathematics tyros. Thanks a lot.

I’m not even in calc yet. I’ve exclusively watched these and can say I have a firm understanding of everything he says. Same for organic chem. Someone get him an award

Thanks for such a great explanation

professor dave thnx for making this video i have my math exam in 3 days and this helped me a lot in learning maxima and minima thank you sir

At last I finally got a video which taught me the concept rather than problems

The holiest video in all of KZread

in the first example is y1 =1 and y2 =-3 ?

My teacher needs to learn from this guy how to explain

hello sir,I want to receive lectures of calculus from you. how can I get that? sir.

Sir excellent method of teaching

Can you tell me in which grade it is studied

Sir. I wanna you that you really helped me understand implicit and relative differenciation

Thank you, Sir Dave!!!

Your intro was awesome!!😅😂😂😂

Thanks for your great explanation.,.👍

You have not made a video about integration by parial fraction decomposition

Professor Dave is like 'Marshmallow of educational field'. He is perfect at every subject 🤯🤯🔥🔥🔥🔥🔥

Great review!

A sent from heaven!! Thank you!!

How did you end up with 1,-1? I’m lost there.

If there are more then 1 local maxima/minima can we find all of them

I had a math question, how can I send it to you?

thank you so much, i was about to cry because i didnt know what to do =)

Very clear, very nice

For the 'comprehension' problem, why did you inset plus 2 and minus 2 into the equation afterwards?

@ProfessorDaveExplains

4 жыл бұрын

because that's where the local maximum and minimum occur, and we want to get the exact maximum and minimum values

this one helps me a lot like im really stuck right now at my calculus. and im very afraid that my top grade goes down. this one really helps sir especially that we are now in new normal class❤❤

Nicely explained

Dave I feel like f prime of X isn't right on 3.46

If there is one job in the world that can be this helpful and important in the world besides medicine it's teaching

But how do we know which root at 3:14 was max or min without a graph?

@srianshuray2861

3 жыл бұрын

check if after differentiation if value more than 0 then minima if value less yhan zero is maxima

About to give up maths but thankyou professor ❤️🥺

I got a little confused at the solution at the end, which of the solutions were maxima and minima'

Any link where I can find a whole. Playlist on applications of differentiation and integration?

@ProfessorDaveExplains

3 жыл бұрын

Check my calculus playlist!

3:10 If the curve is inverted W.R.T x-axis. Then also you will get 2 extrema at x=0 and x=2 But how to tell if that's maxima or minima

@kishorekannan652

Жыл бұрын

Subs value in f(x).. smaller value is minima and maximum value is maxima

I don’t understand for the checking comprehension question. How did you get x=-2? I get how you got 2 but not sure how -2 came about?

@ProfessorDaveExplains

4 жыл бұрын

(-2)^2 is also 4

Explain by profferser Dave is excellent

But, how about how high the local maxima and minima? Is it important?

Thank u *Professor* --😍😍

Thanks bro 👍

I have a question. I know this is a bit late but why did we plug back in 2 and -2 in the f(x) function? Is it because to find the (x,y) values? Please let me know and thank you!

@rxsvie

10 ай бұрын

yup to locate the maximum and minimum points :D

@Theanymemetor

10 ай бұрын

:3@@rxsvie

Also make a video about differential equation

Coming up to my second semester exams and this helps so much. What you do In 6 min takes my teacher 3 lessons

thanks a lot!!!!

Thankyou

Lmaooo I remember learning that topic from this video and now I'm revising it . Nice vid

can someone explain to me why at 3:50 2x^2 disappears?

@tirkdiamond

3 жыл бұрын

Kind of late but in case anyone else is wondering about that : x^2+1 -x *2x = x^2+1 -2x^2 = x^2-2x^2+1 = -x^2+1

Thank you, this was really helpful 😁

Why did I feel like a baby in the first place??

thank you so much

Thank you sir

Can u plz give a simple daily life application of maxima and minina! From many videos i noticed that it helps in economics to maximize and ,in efficienting packing etc..But none of them explains how it is done...well,after finding local maximum,how can it help to maximize profit?!!plz help to figure it out

@9308323

4 жыл бұрын

That's not a "simple daily life application." There's a reason why people study these things for years. However, to answer your question: for this, you'd have to have your revenue and cost function. Subtract the C from R, and from there, just find the local maximum and it should tell you how much you need to set the price for the product. If you want to take it a step further, you can minimize the average cost.

@carultch

2 жыл бұрын

Here's a simple example of optimization, that you could easily understand its application to real life. Suppose we need to transport cargo from an island to a warehouse. Consider a straight shoreline that runs east-west, and the warehouse is L=100 km east of the island, also on the shore. Assume the road runs directly along the shore and any inland travel distance to get to the road is negligible. The island is d=50 km south of the shore. We need to determine where along the shoreline to build our dock for unloading the ship, that will minimize the amount of fuel consumed. Suppose a truck takes 1 liter of fuel to drive 1 km (a rate we can call T) and suppose a ship takes 5 liters of fuel to transport the same cargo a distance of 1 km (a rate we'll call S). Define the origin at the point on the shore directly across the water from the island, and define distance x as the position along this shore where the dock could be located. Assume only a 1-way trip for simplicity. A: find an expression for the fuel consumed by the truck, as a function of dock location x B: find an expression for the fuel consumed by the ship, as a function of dock location x C: find a function f(x) for the total fuel consumed, by combining expressions from parts A and B. Answer: f(x) = T*(L-x) + S*sqrt(x^2 + d^2) D: Take the derivative of this function. E: Set this derivative equal to zero, and solve for the optimal value of x that minimizes fuel consumption. Answer: x=(d*T)/sqrt(S^2 - T^2), which happens at x=10.2 km.

Really it helped 😇

Thanks prof

Professor Jesus helped me pass my class, Thankyou

Thanks bro 👍👍💯🔥🔥🧠

What if the critical point zero

very nice video

You did put the x values once in first derivative and then in the last problem you did put the value in the original function? Why

@robloxeatskids8907

4 жыл бұрын

You find the x values for which the slope is 0 using the derivative and plug those x values into the original function to get the y value.

Ur a blessed soul 🙏

but how find y??

I can just say love u sir..........

How do you find the maximum number of zero crossings?

@pranjalarora3193

10 ай бұрын

Degree of equation= maximum number of zero crossing

Thanks 👍

Are you an actual professor you know everything

@carultch

2 жыл бұрын

He answers this in one of his "Ask Professor Dave" videos.

Thanks from India

How do you find the function when only given the maxima and minima?

@carultch

2 жыл бұрын

You can't. There are an infinite number of functions that have the same minima and maxima.

Lmao i just stared at the video thumbnail for a bit, then i understood exactly what to do 😂😂😂. im just commenting to make sure you know u helped. 👍

Very good

How do we plot (x,y) without using the graph

@carultch

2 жыл бұрын

Your question is self-contradictory. You can't plot a point without a graph.

Helpful 😇

U r good

I just really love intro

This is the entire economics profession

I've passed my calculus classes already, but it's fun to watch it again

very good,

perfecto

professor dave im so sorry i strayed from your teachings i didnt know you had calc lessons

@ProfessorDaveExplains

3 жыл бұрын

Yep 35 part playlist, check it out!

When you set the derivative of the function equal to 0, how do you know which answer is the Maxima/minima??

@ProfessorDaveExplains

4 жыл бұрын

second derivative test!

@ryandelrosario6974

4 жыл бұрын

if its negative it is maxima if its positive it is minima

@7justfun

4 жыл бұрын

@@ProfessorDaveExplains I see the second derivative test uses D = AC - sq(B). Wat do we do for a 4 variate fn?. Also why does it compare D and A , why cant it compare D and C for that matter. A corresponds to x and B to y in f(x.y)

@carultch

2 жыл бұрын

@@7justfun You are probably looking at another meaning of the term "second derivative test" which is not what is meant in this context. In this context, second derivative test refers to the single variable Calculus second derivative test, which means you check the sign of the curvature (i.e. whether it is concave-up or concave-down) in addition to the slope. Given a point where the first derivative is zero, you check the sign of the second derivative to determine whether a critical point is a local maximum or a local minimum. If the second derivative is negative, it is a local maximum, because the function is concave-down (negative curvature). The critical point is at the "top of a hill". If the second derivative is positive, it is a local minimum, because the function is concave-up (positive curvature). The critical point is at the "bottom of a basin". A second derivative of zero is inconclusive. You'll need to check additional derivatives beyond the second derivative. The next even-order derivative (e.g. 4th derivative) that is non-zero will tell you the conclusion of whether it is a local maximum or local minimum. If no additional even order derivatives are positive or negative, then you have an inflection point coinciding with a point of zero slope, as you see in the graph of y=x^3. A point where the concavity switches from being positive to negative, while the slope is simultaneously zero.

Calculus is magic, derivative is fucking wonderfulll!!!!

@tGoldenPhoenix

2 жыл бұрын

Done this lesson.

The intro ❤❤

Sir how to find range 1/√(1-x²)

@carultch

2 жыл бұрын

Start by determining the domain. Forget about imaginary numbers, and focus on real numbers only. What is the minimum x-value, and the maximum x-value that you can plug in to this equation. In order for the square root to be real, the contents of it need to either be positive or zero. This means the maximum x^2 can be is 1, which means x ranges from -1 to +1. However, at these extremes of the domains, we run in to another problem of a zero in the denominator. So our domain is -1 As x approaches these extreme points, the value of the function approaches positive infinity, due to the function being positive just before this, and due to the denominator approaching zero. So this lets us know that y Intuitively, something interesting will also happen at x=0. But we can also prove it by taking the derivative and setting it equal to zero. This allows us to calculate that x=0 is a critical point, which might be a minimum or maximum. d/dx 1/sqrt(1-x^2) = x/(1-x^2)^(3/2) Which equals zero at x=0 Take the second derivative, to determine if this is a minimum or a maximum. d^2/dx^2 1/sqrt(1-x^2) = (2*x^2 + 1)/(1-x^2)^(5/2) Evaluate the second derivative at x=0, and get a positive number, indicating that this is a local minimum. Now evaluate the original function at x=0, to confirm our minimum value of y. 1/sqrt(1-0^2) = 1 We now can conclude that the range is 1

Hi sir! Can help me to solve this problem? Please 🙏🙏🙏 It is so hard for me ☹️ Problem: A rectangular box with a square base is inscribed in a hemisphere of radius R. Find the maximum volume of the box.

@carultch

2 жыл бұрын

Define capital X to be the half-width of the rectangular box. This means that the area of the base of the box will be (2*X)^2. You'll see why we choose to work with the half-width instead of the full width, very soon. We know that X can at a minimum equal zero, and at a maximum equal R, so we will only be interested in critical points within this range. Create an equation for the hemispherical dome, in terms of horizontal positions x and y. Equation of a sphere: x^2 + y^2 + z^2 = R^2 Equation of the positive half of the sphere: z = sqrt(R^2 - x^2 - y^2) Your box will have a corner at a point where y=x, and also equals capital X. Use the previous equation to determine H, the height of the box. H = sqrt(R^2 - 2*X^2) Now define V for the volume of the box: V = H*(2*X)^2 Simplify: V = 4*H*X^2 Plug in H, and now we have our objective equation only in terms of the variable X: V = 4*X^2*sqrt(R^2 - 2*X^2) Take the derivative dV/dX, which we will set to zero to look for the critical value of X where V is maximum. Along the way, you'll be using the product rule, the chain rule, and the power rule. I'll skip the steps and jump right to the result. dV/dX = (8*X*(R^2 - 3*X^2))/sqrt(R^2 - 2*X^2) We are interested in where dV/dX = 0, but we also need to watch out for locations where the denominator is also zero. Because if these coincide, we have a hole in the function instead of a zero. Locations where numerator equals zero: Trivial answer at X = 0, due to 8*X equaling zero at this point. More interesting answer: R^2 - 3*X^2 = 0 Solve for X: X = R/sqrt(3) Denominator of zero: R^2 - 2*X^2 = 0 Solve for X: X = R/sqrt(2) Since these do not coincide, it is acceptable to conclude that X = 0 and X = R/sqrt(3) are our critical points where dV/dX = 0. What ends up happening at X=R/sqrt(2), is that you have the maximum possible square base that can be inscribed in the circle, and its height is zero. We know X=0 is not the maximum, because the box would have no thickness and thus no volume. Therefore, we conclude the critical point X = R/sqrt(3) is the location where the volume is maximized. This means that the box's base dimensions are each equal to 2*R/sqrt(3), and the box's height is R/sqrt(3).

@simon-gh1pt

2 жыл бұрын

@@carultch please help me I have a request to you. How to find maxima and maxima of the type: y=k/f(x) Where f(x)=ax²+bx+c or,|x-a|+|x-b|

@carultch

2 жыл бұрын

@@simon-gh1pt For y=k/(a*x^2 + b*x + c), start by finding the poles of the function (i.e. places where the denominator equals zero). These aren't necessarily the minima/maxima, but they are important points to know. These are locations where there could be a vertical asymptote, meaning the function approaches either positive or negative infinity, or both from opposite sides. This would mean the maximum or minimum is unlimited, as immediately adjacent to the pole, would be an extremely large output. That is, unless a pole coincides with a zero in the numerator, at which point there will be a removable singularity. If there are no real solutions to the denominator equaling zero, it is in your favor, because this means you will have no singularities. Since this is a quadratic expression, we can use the quadratic formula to find where the denominator equals zero. To the tune of pop goes the weasel: "x is equal to negative b, plus and minus the square root; of b squared minus 4*a*c, all over 2*a." Next, we are interested in locations where dy/dx = 0, which means the function will be locally flat, and reach a turning point. Take the derivative, and set it equal to zero. Rewrite as y = k/f(x) dy/df = k*1/f^2 dy/dx = dy/df * df/dx = k/f(x)^2 * f'(x) Take derivative f'(x) = 2*a*x + b, per the power rule. Reconstruct: dy/dx = k*(2*a*x + b)/(a*x^2 + b*x + c)^2 The only way that this function can equal zero, is when 2*a*x + b = 0. Solve for x to be x = -b/(2*a). This will mean that the extreme point will occur at x = -b/(2*a). Take the second derivative and evaluate at x=-b/(2*a), to determine if this is a local minimum (positive 2nd derivative) or a local maximum. This will be the only instance where there is a local extreme point that isn't part of a singularity. The second derivative evaluated at this point equals -(32*k*a^3)/(4*a*c - b^2)^2. When --k*a^3 is positive, you'll have a local minimum. When -k*a^3 is negative, you'll have a local maximum. Note that in the event that b^2 - 4*a*c = 0, then you will also have a denominator equal to zero in the original function at the same point where the derivative equals zero. This means it is inconclusive to call it a local minimum or maximum, because this will also coincide with a vertical asymptote. Ideally, b^2-4*a*c

@carultch

2 жыл бұрын

@@simon-gh1pt As for y=k/(|x - a| + |x - b|), this one has another unique challenge in that the denominator function is not differentiable. There will be kinks/cusps where the interior of the absolute value bars equals zero. This is what you end up with as the derivative: dy/dx = (k*(sgn(a - x) + sgn(b - x)))/(abs(a - x) + abs(b - x))^2 where sgn refers to a function that looks at the sign of the input, and either returns +1 or -1. It returns 0 by convention when the input equals zero. You will also end up with a flat-line between x=a and x=b, so there is an entire range of possible answers for the local maximum or minimum.