I've used your videos for years now and can say that your videos have helped me more then most of my professors have. You should take a lot of pride in knowing you've helped so many people learn math without even seeing there faces. From me and the rest of the community, thank you.
You know what's amazing about how you teach? I can watch a couple of videos and then do my homework without writing down any notes or referencing my textbook, and do well on my quizzes and tests. When I understand something from beginning to end, I have no need to constantly question myself, thank you for being so thorough, it seriously helps.
Wow YOU have to go back to school Justin? What about all that money you made from your acting career? Live free or die hard was such a good movie. Hopefully you're not on the drugs, Justin. You don't want to flush your promising acting career away it's not worth it.
It's 3:30 in the morning where I'm at and I have a math exam at 9. I've been struggling with this stuff and you just totally bailed me out man! You sir are a dream machine! Thanks man!
these simple examples are nice but when it comes to the calculus test the problems are 100x more complex. okay i understand how to find local maxima and minimum for f(x)=x^2 but i go to the test and the question asked find local max/min for f(x)= (sqrt cos(4x) + tan(4x) + x^3/2) / (4 sec^2 (x) * infinity) its like wtf
You are a life saver. I have ad-block on for most of the times, but I really want you to get paid and keep on making these videos. Keep up the great work, and thank you so much!
I wish I found these videos sooner... Got my math final in a few hours. ;_; Thanks for the information though! Been checking out a lot of your videos and they've been really helpful! =)
I've been struggling with on my freshman year of engineering and I can't help but say that i've learned more math out of class then in it. I appreciate you uploading the videos, because you wouldn't believe how much this helps. Thank-you! ^^
Every other video out there is usually an exasperating farrago of misinterpretation distortion and outright lies brodcasted by unprincipled youtubers masquerading like a mathematician but your video provide superb knowledge with easy and helps to convey these concepts to the hoi polloi in no time. With Regards Devang Lal Nehru India
The first I studied this concept (finding min local point by First derivative) was in grade 11. I never understood it (the teachers would never explain it clearly!). You have just cleared up the whole concept for me in 5 minutes. IT WAS THAT EASY? Thank you.
Patrick you're just amazing you've helped me to understand many problems in maths and i really want you to receive my thanking so yeah thank you so much now i really think that maths is easier and better than i thought ... thank you so much ... keep it up and i'm really a big fan of you ... Regards ... Mazen Qomawi from King Fahad University in Saudi Arabia !
U AREEE GREEEEATTTTTTT!!!!!!!!!!!!!!!!... I hope tomorrow I Will pass my calculus exam. I watched all vids about integrals and laplace transform. thank u a lot Patrick!! GOOODD LUCKK GUYSS!
@CCody92 alrighty, i understand. sorry for the ads; the ads are what are helping me sit around all day and make more videos than i ever could have though. without the ads (which make a little $ for me each month), i probably would have made a few hundred less videos this year since i would have been working much more.
Whyyyyy cant my teacher explain it like this! I have went for a month without really knowing what I am doing. When you lay it out like this I can actually understand!
Thank you so much for all the help! I have a blended online Calc class and you've helped me tremendously. I found your website today and donated because I really think you're saving me money in the long run from having to retake this course. If I pass with a good grade at the end of the semester i'll be sure to make a much better donation :)
In middle school i loved math, but in High School my teachers somewhat turned me off of the subject, especially calculus. you sir have rekindled that flame. thanks a ton
just so people understand (and I hope I understand) a critical point is where the derivative equals zero. The derivative is the slope of the tangent line at a particular point. Critical points exist where this slope is zero or undefined, or in a visual sense, the tangent line is horizontal or vertical, horizontal = 0 and vertical = undefined. That's why we set it equal to zero.
thank god for this video, finally now i know how to calculate the freakin increase decrease and concave up and down, a simple god send 10m video. thank you i love you
Because before -1 the graph was decreasing and after -1 as well but there is a small part of the graph at -1 where the graph becomes horizontal (stops decreasing and then starts decreasing again after leaving the point -1) so if you take the tangent at that point it will be a horizontal line whose derivative is zero and that's why its critical. The same goes for 1. And by the way a critical number is not always a max or a minimum, hope this helps :)
I have a question. If f(x) = cos|x| - 2ax +b increases for all x belonging to R, then while calculating f'(x), why do we take it greater than equal to 0 instead of greater than 0.
@patrickJMT I wouldn't have to complain if I had a broadband service (with AT&T) that loaded up the video without me waiting 10+ minutes just to get enough of the video loaded to watch it in small segments and then having to wait another 5 minutes for a 30 second ad to load. I live in rural Mississippi so upgrading is not an option. Ads don't bother me but having to wait 10x longer for the ad to load then it takes to watch the ad does. I do love your videos though.
Heh, small mistake, but: At 2:28, you say, "If you take a number smaller than 1," although the critical number is 0. :P Thanks for your help, regardless, these videos are a big help when it comes to thorough understanding.
Hi Patrick, You just made my day with this video. I was just wondering what would I do if the function was a rational, for example: f(x) = (x-1)/(x^2 + 3).
@dep0303 i also do not particularly for watching the ads on the videos, but that is how people who make the content earn money, allowing them to reinvest/spend more time making videos. glad you like the videos though : ) keep watching the ads : ) i earn pennies a day!
How do you tell if a function is always increasing or decreasing until the next local maximum or minimum without any curves or wiggles in between? The curves can be very vertical which we cannot spot as a critical point.
"I'm going to plug in a number greater than 0, a billion" Idk why but that made me laugh lol. Ty Patrick your examples are going to help me get an A in Calc 1.
For the second equation, how would you write that out the local min/max as a sentence? Would you say At x=0, f(x) has a local minimum of (0,-1)? Is that the correct way to write it out? I'm just asking because I've been wondering and the back of my book doesn't write it out as a sentence, but on my exam next week it will be required to be written out as a sentence. Thanks in advance. :)
I think the reason why I'm just not getting anything up to testing these values is because I literally do not understand the point of Increasing & Decreasing Functions. I mean, what's the concept? How is this applicable? How is this demonstrated? Why do you even test these intervals? There are so many questions left unanswered that I just can't understand anything. I can't just be told what is. This is frustrating.
Local extrema are not absolute if their is another point on the curve that is above/below it. The others are called local/relative because they are extrema on some interval.
great video patrick :) but i have a question: what if the domain of the function was [-1,infinity) and -1 was a critical number and all values of f'(x) for x>-1 are positive, would it still be considered a local minimum or the graph should exist on both sides of it?
oh i had another question, one thnig i've been struggling with is i don't understand what's increasing/decreasing is the function inc./dec. or the slope of the function inc./dec.? i was told to look at the tangent lines from left to right to see if increasing/decreasing and that concave up is increasing for all intervals is that wrong? lol i'm just really confused thnx for all the help!
If there is a line, the only way there could be a max or min is if there was a closed interval. If they said something like, what are the max/mins on [0,5] and they gave you a line of f(x), 0 and 5 would be extrema.
@CCody92 why are you complaining about getting something for free? who do you think pays for this stuff? santa claus? baby jesus? if you do not like the ads, do not watch.
AAH! i had the same question i think JUST got it but i'm not sure, the derivative is equal to zero at max/min.s when it is a horizontal line but i still don't think i completely get it, is there anything i'm missing? Just to get a good understanding THNX!
"I put a number larger than zero... a billion" That escalated quickly.
😆
I've used your videos for years now and can say that your videos have helped me more then most of my professors have. You should take a lot of pride in knowing you've helped so many people learn math without even seeing there faces. From me and the rest of the community, thank you.
You know what's amazing about how you teach? I can watch a couple of videos and then do my homework without writing down any notes or referencing my textbook, and do well on my quizzes and tests. When I understand something from beginning to end, I have no need to constantly question myself, thank you for being so thorough, it seriously helps.
Only resently started watching your calculus videos, they helped me score an A on my last test.
nice mate
Wow YOU have to go back to school Justin? What about all that money you made from your acting career? Live free or die hard was such a good movie. Hopefully you're not on the drugs, Justin. You don't want to flush your promising acting career away it's not worth it.
i assume u dont have an A in english lol
I wish you were my calc teacher.You explain things so well
may I ?
@@hassanasghar5568 you may sir
It's 3:30 in the morning where I'm at and I have a math exam at 9. I've been struggling with this stuff and you just totally bailed me out man! You sir are a dream machine! Thanks man!
thats me 4 years later , It's 3:30 in the morning where I'm at and I have a math exam at 9 woowwww
that is actually cool
The AD: What? Still searching youtube for math help?...
Me: yes and why do u care
these simple examples are nice but when it comes to the calculus test the problems are 100x more complex. okay i understand how to find local maxima and minimum for f(x)=x^2 but i go to the test and the question asked find local max/min for f(x)= (sqrt cos(4x) + tan(4x) + x^3/2) / (4 sec^2 (x) * infinity) its like wtf
marc benedict you actually tells the same thing whats my heart want to tell same here lol !!!!
You are a life saver. I have ad-block on for most of the times, but I really want you to get paid and keep on making these videos. Keep up the great work, and thank you so much!
I want to express my gratitude too. I can learn way better in 10 minutes with you than an hour with my instructor. Thank a lot for your videos.
@obscene678 thanks for the kind words! yes, making the videos makes me feel very happy - so many are so nice to me about them
I wish I found these videos sooner... Got my math final in a few hours. ;_;
Thanks for the information though! Been checking out a lot of your videos and they've been really helpful! =)
did you pass?
hhhhhhhhhhhhh after 2 years you ask him
lol
Zakaria BEGHI But did he pass?
Fourth Reich he probably graduated
I'm having a study party with my people are you are A BEAST!!!! If you were my math teacher I would understand Calc completely.
I have an exam this morning. You're video's have helped me feel confident going into it for once. Thanks for saving my semester.
Going to write my Calculus final in an hour, I love watching your videos for review. Thanks for all your help!
how did ur final go?
@@vexed2418 he failed
With your guidance on these videos patrickJMT; I don't feel so lost in calculus anymore.
I've been struggling with on my freshman year of engineering and I can't help but say that i've learned more math out of class then in it. I appreciate you uploading the videos, because you wouldn't believe how much this helps. Thank-you! ^^
I love it everytime you say "let's take some more complicated examples." hha. thank God you're here to tutor us! :))
Every other video out there is usually an exasperating farrago of misinterpretation distortion and outright lies brodcasted by unprincipled youtubers masquerading like a mathematician but your video provide superb knowledge with easy and helps to convey these concepts to the hoi polloi in no time.
With Regards
Devang Lal Nehru
India
you are helping the whole world in making maths very interesting.God bless you.You are awesome!
The first I studied this concept (finding min local point by First derivative) was in grade 11. I never understood it (the teachers would never explain it clearly!). You have just cleared up the whole concept for me in 5 minutes. IT WAS THAT EASY?
Thank you.
i love u bro u a beast.. a teacher is a job with respect helping out people and the future.. much respect for you
@TheDojojoe glad they all help
Patrick you're just amazing
you've helped me to understand many problems in maths and i really want you to receive my thanking so yeah thank you so much now i really think that maths is easier and better than i thought ... thank you so much ... keep it up and i'm really a big fan of you ...
Regards ... Mazen Qomawi from King Fahad University in Saudi Arabia !
Nice!
thank you so much you did in 3 minutes what my teacher could not in 2 days
@hathorrox spread the word and help make the videos more popular and maybe it will all happen one day : ) glad you like my videos!!
Thanks for the tip at the end!! i now know the difference between local min/max with a neat trick! Won't ever forget now.
U AREEE GREEEEATTTTTTT!!!!!!!!!!!!!!!!... I hope tomorrow I Will pass my calculus exam. I watched all vids about integrals and laplace transform. thank u a lot Patrick!! GOOODD LUCKK GUYSS!
@CCody92 alrighty, i understand. sorry for the ads; the ads are what are helping me sit around all day and make more videos than i ever could have though. without the ads (which make a little $ for me each month), i probably would have made a few hundred less videos this year since i would have been working much more.
aye Patrick i being watching your videos for long time men and they a (GREAT) HELP thank you for doing this peace A-Town.
I love you. lol you are saving me in calculus, I'm using your videos to study for the final. I just wish you were my real calculus teacher :(
@UniqueTrendz yep
Whyyyyy cant my teacher explain it like this! I have went for a month without really knowing what I am doing. When you lay it out like this I can actually understand!
Watching this after class made everything click. 💕🙌🏾
Thank you so much for all the help! I have a blended online Calc class and you've helped me tremendously. I found your website today and donated because I really think you're saving me money in the long run from having to retake this course. If I pass with a good grade at the end of the semester i'll be sure to make a much better donation :)
In middle school i loved math, but in High School my teachers somewhat turned me off of the subject, especially calculus. you sir have rekindled that flame. thanks a ton
you should think about that. what happens on a graph where the derivative equals zero?
just so people understand (and I hope I understand) a critical point is where the derivative equals zero. The derivative is the slope of the tangent line at a particular point. Critical points exist where this slope is zero or undefined, or in a visual sense, the tangent line is horizontal or vertical, horizontal = 0 and vertical = undefined. That's why we set it equal to zero.
Wow I was 3 when this video was published and now 11 years later I’m learning this.
Wow, I was barely one when his was published.
@@awesomecodeyay8382 lol damn u answered 9 months later I’m in high school now😂
@@Ratchet1786 1 you're learning this stuff at 14? Wow
@@superblitz2274 lmao damn this happened a while ago. Y do u wow?
@@Ratchet1786 because this is 12th grade and 1st year uni stuff
thank god for this video, finally now i know how to calculate the freakin increase decrease and concave up and down, a simple god send 10m video. thank you i love you
glad i could help you :)
Because before -1 the graph was decreasing and after -1 as well but there is a small part of the graph at -1 where the graph becomes horizontal (stops decreasing and then starts decreasing again after leaving the point -1) so if you take the tangent at that point it will be a horizontal line whose derivative is zero and that's why its critical. The same goes for 1. And by the way a critical number is not always a max or a minimum, hope this helps :)
tnks ...tmrw is my exam ....
Thanks a lot! Have a test tomorrow, and this vid is my life saver! :D
THanks once agian Patrick, this and the intro to seeing if it is a maxmum or a miminum
My teacher doesnt explain it very well
you do
thanks a lot
literally thank you for saving me in calc. U DA BEST!
i personally love the ads. they add to the mood of the video.
@sHiVeNYu no problem, happy to help : )
Thank you very much ,
and why did you plug in the critical point into the f'(x) not into f(x) like in the absolute extreme values function .
Thanx man... ur amazing... i understand more from you then from my college teachers... :D thumbs up X(a gazillion)
Had to watch this a couple times to understand it, but it really helps.C:
I have a question. If f(x) = cos|x| - 2ax +b increases for all x belonging to R, then while calculating f'(x), why do we take it greater than equal to 0 instead of greater than 0.
@patrickJMT I wouldn't have to complain if I had a broadband service (with AT&T) that loaded up the video without me waiting 10+ minutes just to get enough of the video loaded to watch it in small segments and then having to wait another 5 minutes for a 30 second ad to load. I live in rural Mississippi so upgrading is not an option. Ads don't bother me but having to wait 10x longer for the ad to load then it takes to watch the ad does. I do love your videos though.
Heh, small mistake, but: At 2:28, you say, "If you take a number smaller than 1," although the critical number is 0. :P Thanks for your help, regardless, these videos are a big help when it comes to thorough understanding.
very helpful videos... thank you for all of them!
salutes from mexico
You're so good at teaching!!!! thank you!
Hi Patrick, You just made my day with this video. I was just wondering what would I do if the function was a rational, for example: f(x) = (x-1)/(x^2 + 3).
F'(x) or F(x) we need to choose for looking sign (+ve or -ve) ? Please answer me
you are a lifesaver man thanks.
thank you. you are saving my calc grade!
This is awesome!
Thanks a lot for your efforts.
@dep0303 i also do not particularly for watching the ads on the videos, but that is how people who make the content earn money, allowing them to reinvest/spend more time making videos.
glad you like the videos though : ) keep watching the ads : ) i earn pennies a day!
this video was soooo super helpful! thanks for posting :)
How do you tell if a function is always increasing or decreasing until the next local maximum or minimum without any curves or wiggles in between? The curves can be very vertical which we cannot spot as a critical point.
you are just totally great. Thank you for your hard work and I really appreciate it
Thank you my friend I wasn't sure how to get the coordinates.
You're a great teacher ♥️ God bless you
Ive got my cal final tomorrow, thanks for the help
Yes. If you visualize the graph, 0 has to be an absolute minimum as the graph only increases after it hits that point.
You're wayyy better than my calculus teacher
"I'm going to plug in a number greater than 0, a billion" Idk why but that made me laugh lol. Ty Patrick your examples are going to help me get an A in Calc 1.
I need a 91 on my 2 hour final to pass this class. Currently shitting myself
+Kryptonlte good luck dude.
+Kryptonlte dude I feel you, my exam is tomorrow and I really need to pass
+Kryptonlte gg
+Kryptonlte did u get ur 91?
Brian Joo I got a 96!!! I thought i was so screwed too lol
@baydood510 no, i dont, but do not worry about it : ) skip away, you very thoughtful person.
For the second equation, how would you write that out the local min/max as a sentence? Would you say At x=0, f(x) has a local minimum of (0,-1)? Is that the correct way to write it out? I'm just asking because I've been wondering and the back of my book doesn't write it out as a sentence, but on my exam next week it will be required to be written out as a sentence. Thanks in advance. :)
Thank you for saving my calc grade and life
hi! do you have any video about the positive and negative interval?
no problem!
so once you get the critical points, are you supposed to plug those back into the original equation or the derivative?
This is excellent! I love AP Calc taught this way!
Lol xD I'm watching this 10yr later
Btw I have my exam 2hr later
I think the reason why I'm just not getting anything up to testing these values is because I literally do not understand the point of Increasing & Decreasing Functions. I mean, what's the concept? How is this applicable? How is this demonstrated? Why do you even test these intervals? There are so many questions left unanswered that I just can't understand anything. I can't just be told what is. This is frustrating.
This means you probably don't know derivatives.
I meant you might want to review derivatives before learning this.
That's what homosexuals say to.
dezsaasmith i feel you lol
great vid! helped out a lot!
Local extrema are not absolute if their is another point on the curve that is above/below it. The others are called local/relative because they are extrema on some interval.
You are a life saver!
great video patrick :) but i have a question: what if the domain of the function was [-1,infinity) and -1 was a critical number and all values of f'(x) for x>-1 are positive, would it still be considered a local minimum or the graph should exist on both sides of it?
oh i had another question, one thnig i've been struggling with is i don't understand what's increasing/decreasing is the function inc./dec. or the slope of the function inc./dec.? i was told to look at the tangent lines from left to right to see if increasing/decreasing and that concave up is increasing for all intervals is that wrong? lol i'm just really confused thnx for all the help!
happy to help :)
Your handwriting is neat :D
Thanks for posting! This is definitely helpful!
bro, this is so good. great job
thnx for all these videos... u r awesome
If there is a line, the only way there could be a max or min is if there was a closed interval. If they said something like, what are the max/mins on [0,5] and they gave you a line of f(x), 0 and 5 would be extrema.
You just saved my midterm grade.
@dep0303 ha, come on over. it is a fun town. i really like it here; soooooo many good concerts. (blonde redhead last week rocked!)
@CCody92 why are you complaining about getting something for free? who do you think pays for this stuff? santa claus? baby jesus? if you do not like the ads, do not watch.
This really helped me a lot
Perfect Video! You're the man!
gasp! your left handed? thats awesome(: i wish i was.
thanks for the help! your a life saver
Can't you also do this by plugging critical values into 2nd derivative?
thanks, if negative infinity to 0 is all decreasing, then why are there -1 and +1 as critical points?
Very good...easily understanding concept
AAH! i had the same question i think JUST got it but i'm not sure, the derivative is equal to zero at max/min.s when it is a horizontal line but i still don't think i completely get it, is there anything i'm missing? Just to get a good understanding THNX!