Hey Professor! I just wanted to come here and tell you that my husband just gave me one of the greatest gifts I have ever gotten, one of your shirts!! He always sees me watching your videos, and he knows how helpful you’ve been in my academic career. It made me SO HAPPY to open my gift and seeing “Professor Leonard believes in me.” I’ll be wearing my new shirt for my Calc 3 test next week! You rock!!!
Another Video down! my mom who was going to take the college algebra class with me. She had to drop the class because of how intense the work was over the summer. So now she's watching your videos and getting prepared for the fall semester. Thankyou once again for teaching us math.
I really love and enjoy your videos, Professor Leonard. You made me really enthusiastic about math. I started to study Math every day for 2 hours at least and I am really enjoying it. I'm really thankful for that. After I complete the precalculus course I will study calculus, discrete math, and analysis(abott). I hope I can do it!
Professor Leonard, thank you for the video an Loal Max/Min and Absolute Max and Min in Precalculus and College Algebra terms. I will review these concepts using Calculus for a full understanding.
Professor Leonard, I hope you and your family are doing well. I am going back to get my engineering degree and you are helping out tremendously. Thank you.
Hello Professor Leonard! you're such an amazing teacher....I probably noted that there is a mistake in the Def of local max/min (i think it should be: f(C) is a local max/min, not C ) please consider to correct to me if i'm mistaking... Thank you.
If you read the entire text & the mathematical statement you will see it is 100% correct the 'C' is the condition of f(c).... clearly it IS written: f(x) /= f(c) Min statement & text ONLY then are you introduced to BIG C in a CONDITIONAL STATEMENT qualified by the descriptor of the CHANGE at THAT C POINT [f(c) relative to f(x)] defined viz INCREASING & DECREASING (1st) at the LOCAL INTERVAL being examined AND (2nd) the ENTIRE Canonical Graph as described... so Prof is all correct & if you want to succeed in math, science, engineering, tech fields YOU MUST begin IMMEDIATELY being MORE RIGOROUS & pedantic in reading & re-reading until you are 100% certain you grasp all the info & its consequences- before proceeding with.... whatever [application, answering a question, not blowing up a lab, critiquing the Prof, writing a comment, asking questions, etc etc]... THAT is ESSENTIAL for ANY work of a scientific, technical nature- so by the time you finish this 70+ Pre Calc review you should be brushed up on all concepts, algebra, trig, geometry, etc AND YOU SHOULD NO LONGER BE MAKING ERRORS OF MIS- READING/ MIS- UNDERSTANDING text, mathematical statements, graphs, proofs etc etc... THAT IS AN UNNECESSARY SELF IMPOSED ERROR 100% in your control to correct & so this type of ERROR MUST BE ELIMINATED, by the time you are finished the course... one good way to approach that until corrected is to BREAK EVERYTHING UP IN PIECES: 1. READ THE ENTIRE THING to be examined, answered etc 2. RE- READ & this time BREAK EACH parcel of data into pieces 3. Draw YOUR OWN little graphs [make notes] & RE-WRITE the thing in a different way as if YOU were TEACHING this to someone else & wanted it to be 100% clear [fill in assumed data!] 4. Once complete RE-READ the ORIGINAL AGAIN & then Re-READ what you wrote in the parcels & see if it is 100% understood & correct IF YOU DO THIS over the course of a dozen+ lessons by the time you get past that 12- 20th lesson you will be 100% rigorous at least when it comes to the RUDIMENTARY step of READING & UNDERSTANDING what is written... that will increase your grade simply thru NOT making unnecessary errors & this will prepare you for your career where YOUR mistakes will cost the lab, company, business etc time $$$ & material... which is a NO-NO. In addition by doing this self correction you will be learning an important skill which is problem solving... every time you do something NOT TYPICAL you are learning to THINK & problem solve... so method is as important as smarts when it comes to solving real world problems & taking a step back to consider order of operations, consequences, what is & is not assumed etc will really give you those essential prob solv auxiliary skills or at least fine tune them... Even after you start to see that you are better at READING & understanding 100% BEFORE proceeding with... whatever you will prob continue using something that YOU developed as you engaged in this self correction endeavor... for instance I always try & TEACH what I have learned even if it is in my own mind... by taking that approach I find that I really unlock my abilities [too much to describe] for ex when you re-write something unique from how it was presented to you- it forces you to really understand NOT just a specific problem/concept as you encountered it, but to PLACE IT IN the entire CONTEXT of whatever field it will be applied to... THAT will really accelerate your education & prepare you for the REAL WORLD where there is literally NO answer book or teacher... just you & the prob to solve... Prob Solv is really fun BTW so... developing that skill & those auxiliary skills that lead to greater success & discovering YOUR best way to learn/teaching yourself really... is something that will give you a lot of joy & it is totally NOT dependent upon anyone else... you can even do it in your mind if you were stuck in a wheelchair, stranded on an island or something horrific like that... prob solv is a skill that YOU NEVER have to set aside & you can apply this 100% all the time anytime... in fact you will prob soon see how exhausting being amped up all the time can be & will look forward to winding down... good luck with your studies you aren't just reviewing your math for Calc YOU are learning new ways to LEARN- always [that NEVER stops!]
I am convinced you like absolute value because you like to show off your abs! Seriously, I am a 58 year old, going back to school to finally get my BS and your videos help me tremendously! Thanks. PS You are also vicariously getting me to think about getting back in shape lol.
Hello sir, one the last part of the video , you said there can only be one absolute max and min but in the last example you added two absolute max value instead of adding it to local maximum.
So just as an aside When the world ends I’ll be in Utah Bring a compass The compass will go crazy That’s how you know you’re close The password is “banana”. Love, Christine.
@@maksymandrzejdrzyzgiewicz5096 Yeah, there are some bizarre individuals in the comments section of Professor Leonard's videos. It's deeply discomfiting.
Sir, you write on whiteboard, little c is a local max in definition of local / Relative max and little c is a local min in definition of local / Relative min . But i think f(c) is called local max/min. I don't understand plz clear this concept ! (My english not much better so sorry if any wrong sentence 😀 )
at Valdosta State, somehow having a particular issue with graphs although I'm almost certain it's due to the tenacity of this work and my impatience. Grr
I don't understand how the last graph doesn't have a min, stating that it's never reached, when there is clearly a point that it increases? Doesn't that mean there has to be a lowest point if there is an increase in the graph??
It's because there is an open-point at the lowest point on the graph so that value is never actually achieved. If that point were to be filled in then it would have a min.
Hi, Not understood your 2nd example. Where Local Max : None, Local Min : None, Abs Max : None and Abs Min : -3 @(3,5) Why Local and Abs Max is not (3,5), Can you pl explain ? Thanks
@@paragjp firstly we can't say it is 5, bcz local max or abs max are the points that are on the graph, but here (3,5) is not on the graph, it's been removed, so we can get as close as possible to 5 but not 5. so if u say that ok we can't reach 5, so 4.99 is the max value we can get but then someone will say that no it's 4.999 and another one will say that no it's 4.9999 and it's goes on, since you didn't have an absolute point(5) as a max point in the graph but u can reach as close to it as possible,as the graph is continuous around that point, what ever no u come up with as a max value, there will be another no that is greater than that, that's why we can't have local max or abs max on that particular graph, hope it helps.
Can someone explain how to correctly "think" for the notation used right at the beginning? If based on prev vid: f(x1) < f(x2) means the graph is increasing Here: f(x)
comparing relatively assuming x1=x , x2=c. You can see the output of local max,c is more than the previous point,x or equally difference, hence we produce a peak known as local max, and try to think if the graph is on open interval, which means the graphs continuously propagating without stopping to one point, you will see f(c)>=f(x3), which the graph had to go down at one point where x3>c, but f(x3)
Professor Leonard: Hello. I support your channel and work with a small monthly contribution that will increase when you start linear algebra. You are the best teacher online, BUT can I make a suggestion? Please, write the steps on the board to help students know what to do next. Example: Solve for x. 3x + 3 = 15 1. Subtract 3 from both sides. 2. Divide both sides by the coefficient of x. 3x + 3 - 3 = 15 - 3 3x + 0 = 12 3x = 12 3x/3 = 12/3 x = 4 Can you do this with ALL your sample questions from now on?
Hey Professor! I just wanted to come here and tell you that my husband just gave me one of the greatest gifts I have ever gotten, one of your shirts!!
He always sees me watching your videos, and he knows how helpful you’ve been in my academic career. It made me SO HAPPY to open my gift and seeing “Professor Leonard believes in me.” I’ll be wearing my new shirt for my Calc 3 test next week!
You rock!!!
Awesome! Good luck :)
Wow, you are so lucky 🥺
I can't believe I would ever feel excited and competent when learning math, thank you Professor
Another Video down! my mom who was going to take the college algebra class with me. She had to drop the class because of how intense the work was over the summer. So now she's watching your videos and getting prepared for the fall semester. Thankyou once again for teaching us math.
I really love and enjoy your videos, Professor Leonard. You made me really enthusiastic about math. I started to study Math every day for 2 hours at least and I am really enjoying it. I'm really thankful for that. After I complete the precalculus course I will study calculus, discrete math, and analysis(abott). I hope I can do it!
no you cant
@@quant-prep2843 lol
did you do it?
Hope you did it !
Hello Sir! I am from Turkey and I am a math student. Thank you so much, you helped me and helping me a lot!
Bets lecturer and teacher I have ever come across, He exhudes confidence knowledge of subject matter and mostly, instills a desire to learn
As always, fantastic !
You are the best math teacher in the world. Even for me... An italian. Thanks, Prof
Professor Leonard, thank you for the video an Loal Max/Min and Absolute Max and Min in Precalculus and College Algebra terms. I will review these concepts using Calculus for a full understanding.
you are the best teacher ever.. thank you for making my first year in college easier with your great explanation
Professor Leonard, I hope you and your family are doing well. I am going back to get my engineering degree and you are helping out tremendously. Thank you.
Hello Professor Leonard! you're such an amazing teacher....I probably noted that there is a mistake in the Def of local max/min (i think it should be: f(C) is a local max/min, not C )
please consider to correct to me if i'm mistaking...
Thank you.
If you read the entire text & the mathematical statement you will see it is 100% correct the 'C' is the condition of f(c).... clearly it IS written:
f(x) /= f(c) Min statement & text
ONLY then are you introduced to BIG C in a CONDITIONAL STATEMENT qualified by the descriptor of the CHANGE at THAT C POINT [f(c) relative to f(x)] defined viz INCREASING & DECREASING (1st) at the LOCAL INTERVAL being examined AND (2nd) the ENTIRE Canonical Graph as described... so Prof is all correct & if you want to succeed in math, science, engineering, tech fields YOU MUST begin IMMEDIATELY being MORE RIGOROUS & pedantic in reading & re-reading until you are 100% certain you grasp all the info & its consequences- before proceeding with.... whatever [application, answering a question, not blowing up a lab, critiquing the Prof, writing a comment, asking questions, etc etc]... THAT is ESSENTIAL for ANY work of a scientific, technical nature- so by the time you finish this 70+ Pre Calc review you should be brushed up on all concepts, algebra, trig, geometry, etc AND YOU SHOULD NO LONGER BE MAKING ERRORS OF MIS- READING/ MIS- UNDERSTANDING text, mathematical statements, graphs, proofs etc etc... THAT IS AN UNNECESSARY SELF IMPOSED ERROR 100% in your control to correct & so this type of ERROR MUST BE ELIMINATED, by the time you are finished the course... one good way to approach that until corrected is to BREAK EVERYTHING UP IN PIECES:
1. READ THE ENTIRE THING to be examined, answered etc
2. RE- READ & this time BREAK EACH parcel of data into pieces
3. Draw YOUR OWN little graphs [make notes] & RE-WRITE the thing in a different way as if YOU were TEACHING this to someone else & wanted it to be 100% clear [fill in assumed data!]
4. Once complete RE-READ the ORIGINAL AGAIN & then Re-READ what you wrote in the parcels & see if it is 100% understood & correct
IF YOU DO THIS over the course of a dozen+ lessons by the time you get past that 12- 20th lesson you will be 100% rigorous at least when it comes to the RUDIMENTARY step of READING & UNDERSTANDING what is written... that will increase your grade simply thru NOT making unnecessary errors & this will prepare you for your career where YOUR mistakes will cost the lab, company, business etc time $$$ & material... which is a NO-NO.
In addition by doing this self correction you will be learning an important skill which is problem solving... every time you do something NOT TYPICAL you are learning to THINK & problem solve... so method is as important as smarts when it comes to solving real world problems & taking a step back to consider order of operations, consequences, what is & is not assumed etc will really give you those essential prob solv auxiliary skills or at least fine tune them...
Even after you start to see that you are better at READING & understanding 100% BEFORE proceeding with... whatever you will prob continue using something that YOU developed as you engaged in this self correction endeavor... for instance I always try & TEACH what I have learned even if it is in my own mind... by taking that approach I find that I really unlock my abilities [too much to describe] for ex when you re-write something unique from how it was presented to you- it forces you to really understand NOT just a specific problem/concept as you encountered it, but to PLACE IT IN the entire CONTEXT of whatever field it will be applied to... THAT will really accelerate your education & prepare you for the REAL WORLD where there is literally NO answer book or teacher... just you & the prob to solve...
Prob Solv is really fun BTW so... developing that skill & those auxiliary skills that lead to greater success & discovering YOUR best way to learn/teaching yourself really... is something that will give you a lot of joy & it is totally NOT dependent upon anyone else... you can even do it in your mind if you were stuck in a wheelchair, stranded on an island or something horrific like that... prob solv is a skill that YOU NEVER have to set aside & you can apply this 100% all the time anytime... in fact you will prob soon see how exhausting being amped up all the time can be & will look forward to winding down... good luck with your studies you aren't just reviewing your math for Calc YOU are learning new ways to LEARN- always [that NEVER stops!]
@@MrAdamNTProtester when the Adderall peaks
@@MrAdamNTProtester yo thanks a lot for this
I legit am just here for fun! Thanks so much for the help and the content ❤❤❤
sir you are best teacher as compare to an other
One of the best teacher even though I got distracted couple of time I still understand fully
So this is what Clark Kents' been doing in his part-time.
Professor Leonard, You can't guess the amount of respect I have for you in my heart.
reallly ? then send him 1 dollar
I love your method of teaching
Hi professor big fan of yours please keep making great videos
Mee2
I really really appreciate these videos! Thank you from the bottom of my heart.🤗🤗
is there a channel like this for Physics, that uploads full-length physics videos?
Patrickjmt
The Organic Chemistry Tutor
"Michel Van Biezen".
checkout Professor Walter Lewin's channel
@@ders8834 they have saved my life in legit three separate classes I have taken
Read History if you cant believe Every Leonard is a Legend AND SO YOU ARE
lot of respect from Nepal
Hi sir u r such a great teacher i ever seen 😍 stay blessed
I am convinced you like absolute value because you like to show off your abs! Seriously, I am a 58 year old, going back to school to finally get my BS and your videos help me tremendously! Thanks. PS You are also vicariously getting me to think about getting back in shape lol.
Hello sir, one the last part of the video , you said there can only be one absolute max and min but in the last example you added two absolute max value instead of adding it to local maximum.
great lecture Leonard, just like all your videoes!
hello professor can you please make videos on linear algebra , that will be very helpful .
thank you in advance !
So just as an aside
When the world ends
I’ll be in Utah
Bring a compass
The compass will go crazy
That’s how you know you’re close
The password is “banana”.
Love,
Christine.
Please explain, I can't sleep because of this
@@maksymandrzejdrzyzgiewicz5096 Yeah, there are some bizarre individuals in the comments section of Professor Leonard's videos. It's deeply discomfiting.
@@maksymandrzejdrzyzgiewicz5096 she's a prepper with a bunker in Utah and wants to welcome good genes for the afterMath
Shouldn't I have put the brackets in the ABS values??? for example [5]@(5,5)
If output is the local or absolute extrema, then why write the input c as the local min and max in your write up?
hi professor, first of all, thank you so much for your work... and how many videos are remaining to complete the Pre-calculus playlist ??
Had me dying at 11:22 😂😂😂.
Hi, How long will this series be? Also how many videos are you planning to do for each algebra and trigonometry
Thank you!
Sir, you write on whiteboard, little c is a local max in definition of local / Relative max and little c is a local min in definition of local / Relative min .
But i think f(c) is called local max/min. I don't understand plz clear this concept !
(My english not much better so sorry if any wrong sentence 😀 )
at Valdosta State, somehow having a particular issue with graphs although I'm almost certain it's due to the tenacity of this work and my impatience. Grr
i see an absolute maximum on those biceps
These are great, but hoping we'll get the full on hour long classes soon:-)
I don't understand how the last graph doesn't have a min, stating that it's never reached, when there is clearly a point that it increases? Doesn't that mean there has to be a lowest point if there is an increase in the graph??
It's because there is an open-point at the lowest point on the graph so that value is never actually achieved. If that point were to be filled in then it would have a min.
sir - is there any video(s) for linear algebra for beginner ?
Hi, Not understood your 2nd example. Where Local Max : None, Local Min : None, Abs Max : None and Abs Min : -3 @(3,5) Why Local and Abs Max is not (3,5), Can you pl explain ? Thanks
Abs Min:-3 @(0, -3) Thanks
@@paragjp firstly we can't say it is 5, bcz local max or abs max are the points that are on the graph, but here (3,5) is not on the graph, it's been removed, so we can get as close as possible to 5 but not 5. so if u say that ok we can't reach 5, so 4.99 is the max value we can get but then someone will say that no it's 4.999 and another one will say that no it's 4.9999 and it's goes on, since you didn't have an absolute point(5) as a max point in the graph but u can reach as close to it as possible,as the graph is continuous around that point, what ever no u come up with as a max value, there will be another no that is greater than that, that's why we can't have local max or abs max on that particular graph, hope it helps.
I have an irrational fear of functions.
Rationalize it, use conjugates! ))
Even rational functions?
3:00
Can someone explain how to correctly "think" for the notation used right at the beginning? If based on prev vid:
f(x1) < f(x2) means the graph is increasing
Here:
f(x)
comparing relatively assuming x1=x , x2=c. You can see the output of local max,c is more than the previous point,x or equally difference, hence we produce a peak known as local max, and try to think if the graph is on open interval, which means the graphs continuously propagating without stopping to one point, you will see f(c)>=f(x3), which the graph had to go down at one point where x3>c, but f(x3)
April 1 2022
Do you use Instagram professor Leonard?
next absolute value please
Came here for "why"
Do you need to listen to these after you create them to find the mistakes. There’s a mistake at 2000
10
day 2
First
"что бы в эс сосалось"
Professor Leonard:
Hello. I support your channel and work with a small monthly contribution that will increase when you start linear algebra. You are the best teacher online, BUT can I make a suggestion? Please, write the steps on the board to help students know what to do next.
Example:
Solve for x.
3x + 3 = 15
1. Subtract 3 from both sides.
2. Divide both sides by the coefficient of x.
3x + 3 - 3 = 15 - 3
3x + 0 = 12
3x = 12
3x/3 = 12/3
x = 4
Can you do this with ALL your sample questions from now on?
I am somewhat of an extremist myself, actually ))
You need to be constantly checking these videos for things that you say that are not correct
I'm from Pakistan