Caleb Harrison That's great! I'm really glad to hear that you're happy with your instructor! The more good teachers we have, the better educated future generations will be. Enjoy! P. Leonard
Caleb Harrison That's fantastic but if your instructor/professor is so great then why surf youtube for calculus videos? Just saying. These are invaluable resources for non-traditional students. Much luck in your Calculus career. Cheers.
Professor Leonard , I'm not sure if I got this right, but the graph you were working on from 28:00 and on..., isn't the concavity of that graph increasing from neg-infinity to approximately negative one? If the graph is going from left to right, shouldn't the slope be increasing from (-infnty, -1)?
Leonard, I can't tell you how grateful I am that you exist. let me tell you how much easy you have made my life, maths is my all times favorite subject now. I pray you live a long and happy life, so that you can continue making students' life easy all around the world. please keep posting more brilliant videos. I am struggling a bit in trig: I hope you read this and I'll really appreciate if you reply.
+Maha Agro Hi, thanks for the comment!! Videos are always in the works, and Calc 3 is being posted this semester. I have some other projects in the works, and I hope that Trig becomes a little more understandable for you. Good Luck!
Sir, you are not only raising the education standard of your own country but the world. I am enjoying Calculus here in India. Your youtube channel is probably the best place on the Internet. Thank you for the lectures.
Instead of music when practicing other stuff, I just listen/watch these. When I do come and give 100%, I already understand about 30-60% of the video. Keep being the Calculus 🐐
I feel extremely fortunate to have you for pre-algebra, trig, calc 1, calc 2, calc 3, and differential equations. Maybe linear algebra is coming?! Seriously though, thank you for doing SO much! You’re getting me through my statistics and comp sci degree.
Prof Leonard, you've got a gift for teaching. Thank you so much for helping us all get through math class! By the way, keep telling jokes because you've got a witty sense of humour.
Thank you so much!!!! Sometimes I need to be taught like I'm a 5 yr old...very simple, absorbent, and concise...I actually have hope of passing my online class.
I think an easy way to represent concavity is through velocity and acceleration. You may have a negative velocity but you can still be accelerating/decelerating and vice-versa.
Thank you Mr. Leonard. I credit your style of explaining Calculus for my new found confidence in applying the Product, Quotient, and Chain Rules, Differentiation by Substitution, Implicit Differentiation, and Related Rates; and now Concavity. Part of it for me, I think, is in the way you speak of the common mistakes you see and warn against doing them. Like when you've warned against distributing terms that are not distributable. With this concavity, there are times when the slope is decreasing in the mathematical sense while it is getting steeper in a graphical sense as at point c at 35:00 in this video. Where the graph is getting more steep in the negative direction the slope is decreasing. To the graphical mind this may be an initial stumbling block. Also your "follow the d/dx" has been very helpful to me. Thanks again.
I love maths but then there are most times i can't do things myself. We don't have proper classes (offline or online) in India which sucks honestly. But i love your explanation the most. I've been searching for an english free tutor for a long time, then with God's grace i found you sir Leonard. I am in grade 12 currently and this it so helpful. Thank you sir!❤
You are the GOAT. The real MVP. So easy to understand when you explain it. Thank you professor, you saved me and a whole bunch of other students from struggling. I am now striving for an A in my calc math class.
It is a point where something interesting happens, because the original function has a vertical slope at this point. It is interesting, but frustrating, behavior of the function.
Leonard, Thank You for making these awesome videos. The way you teach is very effective and fun. Also, making these videos free was the best part, some people are at a financial disadvantaged, and it's good to see there are still people who are this smart and still like to help others without expecting something in return($$) . Honestly I have never had teacher that can teach as effectively as you do and never expect to. Hope the best for your future! Keep on doing GREAT things!!!
at 1:15:32 solution of x^(-2/3)=0 will not give x=0 as solution. In fact it will give 1/x^2=0 so x has to go to infinity for 1/x^2 to be 0. In fact at x=0 the slope is not defined. It is still a critical number
At 1:17:56, why is the function not undefined at -1? Wouldnt that give a root with a negative in it? My calculator even gives me a domain error when I put it in.
this is awesome!!!!! i can't believe calculus could be this interesting. thanks Sir. i'm going to tell my friends about your videos.... and yeah they will loveeeeee it!!!
Hey Mr. Professor Leonard. Thanks a lot for your lecture, i watch this series really carefully. But i think on the 1:15:40, at x=0 this function is not differentiable. Because x^-2/3--------> 1/x^2/3. Denominator cannot be 0 :)
Calc exam tomorrow, and I'm in the middle of an amphetamine powered study extravaganza that'll last at least 10 hours. BLESS THIS MAN FOR MAKING THESE VIDEOS. These are the damage control for my poor decision making : ' ]
Sir ur way of teaching is fabulous..but as I m learning calculus for the first time..so plz add subtitles on all ur videos for calculus...I will very thankful for this.
Respected Professor Leonard, I am very grateful to you for sharing such type of great knowledge. I hope you will must go ahead to keep help of younger. But I am confused on 47:00 to "If you have a denom, set denom=0 as well" What does it mean. I am not a native speaker may be it is due to language difference. If you please could not mind and can explain me I will be very thankful to you.
There is a break at 19:56 where he comes back and it is clear that some material has been skipped. There was no prior discussion about the 2nd derivative test, so this feels a little confusing... like we missed part of a lecture.
Just have a question is it really x=0, when you take the value of x in x raise to the negative two thirds = 0. Is there a specific rule in it? When I use calculator it shows undefined and as I also try to calculate it it seems that it will result to 1/x^2/3 = 0 which means that if x is 0 then 1/0 is undefined. By the way this channel is great!!
Thanks a lot for such quality lectures. It's really helping me and my friends a lot. Really I can't express how thankful I'm to you. Btw which book do u recommend for practicing problems? Please let me know sir. Once again thanks a lot. 🙏
Around that part, I thought (-infinity,0) were indicating the coordinate, until he wrote inflection point x =1. Then I know it was increasing from -infinity to 0, but not the function at the point (-infinity,0) was increasing.
also what do you mean by holds water... I think of holding water as in MY COUSIN VINNY "does the defense hold water?" is that how you meant holding water? like the poetic metaphor way or do you mean curved shaped to fill up with liquid water that can be transported and saved for another moment in the future?
Random question, but is this the same class throughout the entire Calculus series? I mean litearlly the kids he's teaching...is it the same bunch through the whole class?
wow.... I just came up with a genius idea... the double like button... only the God's can receive such an applause. how freakin awesome is it that an exponential function is constantly climbing? like its a U shape and even when it goes down its really going up bc its just less negative less negative less negative, pause (Nate dogs voice) HOLD UP, positive more positive more positive... poopie caca I say gosh... its not difficult to think of its just very odd its like trying to remember a dream its cloudy and its like wait the truth is right in front of me I just need to clear more of this gases mist smoke in the way
Does anyone have a link to the type of sign analysis test that's done round 1:25:30? I've done sign analysis for inequalities but I can't see how plugging in two random "test" x-values close to the asymptotes necessitates that the sign of the entire interval is the same as the output of the test values . . .
@@AliSeyed I think you're right, instead of factoring I turned the exponents into fractions with surds then added the fractions, now equating to zero, only the numerator would lead to zero, even on the calculator 0^(-2/3) = Math Error. I am not sure how the professor concluded x could equal zero. However, I also took the denominator into consideration to determine where the slope is undefined (equated it to zero). And THAT's where x=0.
![[DOKKAN BATTLE] Worldwide Campaign Announcement Video Part 2!](http://i.ytimg.com/vi/JpT5Voak6WA/mqdefault.jpg)
Probably the best calculus instructor in the world
Caleb Harrison
That's great! I'm really glad to hear that you're happy with your instructor! The more good teachers we have, the better educated future generations will be. Enjoy!
P. Leonard
Professor Leonard
I honestly don't think there could be anyone better than this guy P. Len
Caleb Harrison That's fantastic but if your instructor/professor is so great then why surf youtube for calculus videos? Just saying. These are invaluable resources for non-traditional students. Much luck in your Calculus career. Cheers.
Professor Leonard Your a gangster come get a job in colorado.
Professor Leonard , I'm not sure if I got this right, but the graph you were working on from 28:00 and on..., isn't the concavity of that graph increasing from neg-infinity to approximately negative one? If the graph is going from left to right, shouldn't the slope be increasing from (-infnty, -1)?
Leonard, I can't tell you how grateful I am that you exist. let me tell you how much easy you have made my life, maths is my all times favorite subject now. I pray you live a long and happy life, so that you can continue making students' life easy all around the world. please keep posting more brilliant videos. I am struggling a bit in trig: I hope you read this and I'll really appreciate if you reply.
+Maha Agro Hi, thanks for the comment!! Videos are always in the works, and Calc 3 is being posted this semester. I have some other projects in the works, and I hope that Trig becomes a little more understandable for you. Good Luck!
thanks very much Leonard :)
I can’t believe I’m watching this for free. Goodness, I’m so grateful for having access to such tutoring lessons.
Sir, you are not only raising the education standard of your own country but the world. I am enjoying Calculus here in India. Your youtube channel is probably the best place on the Internet. Thank you for the lectures.
I was sick and subsequently missed over a month of class. I was still able to make an 87 on my last exam because of your lectures. Thank you so much!
Instead of music when practicing other stuff, I just listen/watch these. When I do come and give 100%, I already understand about 30-60% of the video. Keep being the Calculus 🐐
I feel extremely fortunate to have you for pre-algebra, trig, calc 1, calc 2, calc 3, and differential equations. Maybe linear algebra is coming?!
Seriously though, thank you for doing SO much! You’re getting me through my statistics and comp sci degree.
I'm 43 and taking Calculus for the first time in my life, this guy is helping me out so much
Leonardo ,a person with both brain and muscles
All the people
brains and gains
Prof Leonard, you've got a gift for teaching. Thank you so much for helping us all get through math class! By the way, keep telling jokes because you've got a witty sense of humour.
So glad this dude decided to upload all these. I think I am going to go support his patreon bc he is a lifesaver.
did u evr donate
Some people where born to impact others Sir, this is yyour calling and you are doing excellently well!
You have great conceptual clarity and thats the way maths should be taught..
Thanks ..Respect (from India)
Thank you so much!!!! Sometimes I need to be taught like I'm a 5 yr old...very simple, absorbent, and concise...I actually have hope of passing my online class.
I think an easy way to represent concavity is through velocity and acceleration. You may have a negative velocity but you can still be accelerating/decelerating and vice-versa.
Professor, you are awesome, your level of enthusiasm and your level of energy for teaching calculus tends to infinity. limit -> infinity. Love you.
Relative Extrema 37:01 Absolute extrema 50:00
1:19:41 for the x^{-2/3}, isn't x can't be 0 because if it's 0, then it will become 1/0 because of negative exponent?
Yes, I noticed that as well.
Thank you Mr. Leonard.
I credit your style of explaining Calculus for my new found confidence in applying the Product, Quotient, and Chain Rules, Differentiation by Substitution, Implicit Differentiation, and Related Rates; and now Concavity. Part of it for me, I think, is in the way you speak of the common mistakes you see and warn against doing them. Like when you've warned against distributing terms that are not distributable. With this concavity, there are times when the slope is decreasing in the mathematical sense while it is getting steeper in a graphical sense as at point c at 35:00 in this video. Where the graph is getting more steep in the negative direction the slope is decreasing. To the graphical mind this may be an initial stumbling block. Also your "follow the d/dx" has been very helpful to me. Thanks again.
I love maths but then there are most times i can't do things myself. We don't have proper classes (offline or online) in India which sucks honestly. But i love your explanation the most. I've been searching for an english free tutor for a long time, then with God's grace i found you sir Leonard. I am in grade 12 currently and this it so helpful. Thank you sir!❤
This is an AWESOME video for going over these concepts. Easily confused! You made it so easy to follow! Love it!
You are the GOAT. The real MVP. So easy to understand when you explain it. Thank you professor, you saved me and a whole bunch of other students from struggling. I am now striving for an A in my calc math class.
Best lecturer ever ❤what i failed to learn in 9 weeks learnt it in Just a week long live professor leonard
Thank you for all of these, from the bottom of my little black heart.
I am having straights A's in Calculus. Thank you sir!
x = 0 cannot be a critical point. x^(-2/3) = 0 does not yield any solutions. Other than that, this was a wonderful lecture. Thank you!
It is a point where something interesting happens, because the original function has a vertical slope at this point. It is interesting, but frustrating, behavior of the function.
Leonard, Thank You for making these awesome videos. The way you teach is very effective and fun. Also, making these videos free was the best part, some people are at a financial disadvantaged, and it's good to see there are still people who are this smart and still like to help others without expecting something in return($$) . Honestly I have never had teacher that can teach as effectively as you do and never expect to. Hope the best for your future! Keep on doing GREAT things!!!
I'll be starting chapter 3 of Calc1 this semester, and this thing is a huge help for me! Thank you prof leonard!
BEST Instructor I have ever seen...
woaw i can't believe such a thing is here!!!!!!....good work. I now find my studies so easy, keep it up.
I hope linear algebra will be posted soon.
at 1:15:32 solution of x^(-2/3)=0 will not give x=0 as solution. In fact it will give 1/x^2=0 so x has to go to infinity for 1/x^2 to be 0. In fact at x=0 the slope is not defined. It is still a critical number
what is X^2=0? Or even X^3=0
@@elizabethatienootieno3083
In both those cases, x = 0.
was looking for this comment thanks!
Omg,such a great teacher... Thanks a lot prof.Respect for you sir #from 🇮🇳
I love when I catch myself answering his questions when I watch these vids at the library.
At 1:15:27 how do we equate x to the negative power to 0. Isnt it undefined?
I just can't emphasis how thankful I am.
Mr. Leonard, you're one in a million. I'm getting A in calculus 1 this semester because of you. I have to go for my fees and bring it to you
hey professor... i loved your videos a lot... thanks for all these stuff.. lots of love from India.
I want the autograph of the student who sneezes every video
lol and he never acknowledges the kid either it is so funny
AirIndy5000 I
when did he sneeze
@@ivantasticforever 24:00
And cough too
Omg Iam a freshman now and u saved my life thank you so much.
At 1:17:56, why is the function not undefined at -1? Wouldnt that give a root with a negative in it? My calculator even gives me a domain error when I put it in.
your expertise is not only math, but an outstanding math educator as well. Thanks for sharing your knowledge.
this is awesome!!!!! i can't believe calculus could be this interesting. thanks Sir. i'm going to tell my friends about your videos.... and yeah they will loveeeeee it!!!
Hey Mr. Professor Leonard. Thanks a lot for your lecture, i watch this series really carefully. But i think on the 1:15:40, at x=0 this function is not differentiable. Because x^-2/3--------> 1/x^2/3. Denominator cannot be 0 :)
Yes you are correct.
Calc exam tomorrow, and I'm in the middle of an amphetamine powered study extravaganza that'll last at least 10 hours. BLESS THIS MAN FOR MAKING THESE VIDEOS. These are the damage control for my poor decision making : ' ]
lol
did u pass
i think u failed
u failed
@@jensmalzer6344 it’s been 3 years dawg are you good
Sir ur way of teaching is fabulous..but as I m learning calculus for the first time..so plz add subtitles on all ur videos for calculus...I will very thankful for this.
Respected Professor Leonard, I am very grateful to you for sharing such type of great knowledge. I hope you will must go ahead to keep help of younger. But I am confused on 47:00 to "If you have a denom, set denom=0 as well" What does it mean. I am not a native speaker may be it is due to language difference. If you please could not mind and can explain me I will be very thankful to you.
He means DENOMINATOR of a fraction !!! If you are working on a problem and you have a fraction, you need to set the denominator to zero !!!
I was pretty confused as well. He never gave an example of a function with a denominator, so I'm not entirely sure what he's talking about.
There is a break at 19:56 where he comes back and it is clear that some material has been skipped. There was no prior discussion about the 2nd derivative test, so this feels a little confusing... like we missed part of a lecture.
@1:20:15 I think one of his students messed up the f(x) for -1, its supposed to be -3 not 9
I was going over it again and again thinking the same.
Prof Leonard, I just want to say thank you.
Thank you so much! I finally learned this after 2 months of struggling
You are a hero!! The best teacher ever!
i swear to god, you make everything seem so easy when you teach it
Sir plz add turned on the subtitles on this video..as on some videos subtitles are given..so its easy for students to understand.
You are already doing more work than my actual professor. You may be the only reason I survive this semester.
RUclips is my collage
Ali Kasem to bad they don't have English lessons
"to bad" the irony lol
@@andresramirez5306 lmfaooo comedy
@@andresramirez5306 I'm dead 💀
29:30 with comeback of the year. Good job teach
Which foul creatures dislike the video.
Probably some other math professors
😂😂😂😂😂😂
@@dollieelizabethjames343 dey jelly
@Jose Jimenez LOL!
relative to what the graph is doing at that part of the graph
Just have a question is it really x=0, when you take the value of x in x raise to the negative two thirds = 0. Is there a specific rule in it? When I use calculator it shows undefined and as I also try to calculate it it seems that it will result to 1/x^2/3 = 0 which means that if x is 0 then 1/0 is undefined. By the way this channel is great!!
Thanks a lot for such quality lectures. It's really helping me and my friends a lot. Really I can't express how thankful I'm to you. Btw which book do u recommend for practicing problems? Please let me know sir. Once again thanks a lot. 🙏
I had to go one chapter without you. Had to put in extra work. (Tho I found some of your stuff in calc 2 lol) but glad to have this back. Yay !
One of the best PRO Professors i have ever seen 👏👏👏👏
one of my favourit teacher
Thank you so muchhhh :< I did not even notice the video was 8 years old already
Professor Leonard, I am curious to know just how to cube root in my head (LIKE YOU DID) without a calculator? (Serious inquiry)
calculus tastes something else with prof. Leonard ❤
Is this section the Extrema on an Interval because this is what i have for 3.1- Extrema on an Interval
ive got a calc test next week, and while my professor is good, the test will be really hard. thanks for helping me prep for it.
U R THE BEEEST, THANKS
Excellent lecture, totally saved my bacon!
This man is a hero !
"You could be straight, but that's not fun." -Professor Leonard 2014
Around that part, I thought (-infinity,0) were indicating the coordinate, until he wrote inflection point x =1. Then I know it was increasing from -infinity to 0, but not the function at the point (-infinity,0) was increasing.
Could you please turn on captions for this video?
also what do you mean by holds water... I think of holding water as in MY COUSIN VINNY "does the defense hold water?" is that how you meant holding water? like the poetic metaphor way or do you mean curved shaped to fill up with liquid water that can be transported and saved for another moment in the future?
Hey - so relative extrema is based on the y-axis whereas concavity is based on the x-axis?
Mr.Leonard,your videos are great.Can you make videos on Higher Algerbra please?
local extrema and relative extrema both are same or not????
Yes
2021 math and we have leonard professor yay!
professor did a mistake at 1:27:50 he wrote (x^2-1)^-1 but it should be (x^2-x)^-1
Samsher Singh I was looking for this comment, thank you
That's what you would get after you've taken the derivative. He didn't mess up
@@bobjoe164 but he didn't take derivative yet.... but yea he wrote it correctly in the next step
Random question, but is this the same class throughout the entire Calculus series? I mean litearlly the kids he's teaching...is it the same bunch through the whole class?
wow.... I just came up with a genius idea... the double like button... only the God's can receive such an applause. how freakin awesome is it that an exponential function is constantly climbing? like its a U shape and even when it goes down its really going up bc its just less negative less negative less negative, pause (Nate dogs voice) HOLD UP, positive more positive more positive... poopie caca I say gosh... its not difficult to think of its just very odd its like trying to remember a dream its cloudy and its like wait the truth is right in front of me I just need to clear more of this gases mist smoke in the way
Is there a way to access the home-works @Professor Leonard gives his students at the end of each lecture so that we can all follow through.
i'd like to know too
29:30. Damn. You got me. LOL.
من طرف احمد علي 😍👌
I might be in love with you Professor. Thank you for making this a hell lot easier!
In the future, I want to be like you Professor Leonard.
Really great, Thanks
how do you find out the interval? And if it is all real numbers how do you get an absolute max or minEx.) 2x^2 +3x-2 absolute min.= -(25/8) how?
Your vids never fail to make me concave up 😊
Best professor ever
Thank you so so much for these videos!! You rock!
Does anyone have a link to the type of sign analysis test that's done round 1:25:30? I've done sign analysis for inequalities but I can't see how plugging in two random "test" x-values close to the asymptotes necessitates that the sign of the entire interval is the same as the output of the test values . . .
Thank you. Your videos are very helpful
you're the best, professor Leonard
i don't think the problem he is doing at 1:21:49 has an absolute maximum. the origin of the functions is at 0
I couldn't understand how this x^(-2/3)=0 has an answer zero at 1:15:25 ? Because x goes to denominator, how come 1/sth be equal to 0?
@Professor Leonard
@@AliSeyed I think you're right, instead of factoring I turned the exponents into fractions with surds then added the fractions, now equating to zero, only the numerator would lead to zero, even on the calculator 0^(-2/3) = Math Error. I am not sure how the professor concluded x could equal zero. However, I also took the denominator into consideration to determine where the slope is undefined (equated it to zero). And THAT's where x=0.
You're awesome.
very batter lecture I learn first time in my life, thanks sir ,i see your lecture form Bangladesh.
Pranam sir 🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏🙏