Difference Quotient
Вставка
- Опубліковано 9 лют 2025
- PreCalculus introduction to the Definition of the Difference Quotient
Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage / profrobbob
I have wanted to say a HUGE "THANK YOU" to you Professor RobBob for your generosity in posting such GREAT math tutorials. You do it in a very clear and organized manner. Not only are your students benefiting from your clarity and organized presentation of often confusing concepts, but the ENTIRE online community benefits as well - that's GENEROSITY!! Thank you so much for your excellent math tutorials!! ❤ "BAAAMM!!" - now I'm gonna go do my homework 😄
YOU'RE WELCOME R May...and thanks for taking the time to study outside the classroom, choosing my channel to learn from and sharing your appreciation with us! Students like you are why we work so hard to keep this channel growing....so we continue ask for your help by sharing this channel with your friends, classmates and especially your teacher so ALL current and future students know where to find free math help!!! And please remind everyone how important it is to like, SUBSCRIBE and share these helpful educational channels thru social medias because that's how we grow and remain free for everyone.
So BAM!!!...start sharing!!!
I swear this guy explained to me in 15 minutes, what my teacher couldn't do in a 2 hour study session, thank you ProfRobBob.
Happy I could help…Thanks for supporting by watching and subscribing:)
WOW...thank you again for such a wonderful review. I really do appreciate all the support from my subscribers, doing these videos after a full day of teaching is very time consuming (just ask my wife) but the end goal, and the uplifting comments make it easy to continue. With the help of people like you spreading the word...my channel will continue to grow bigger and bigger and help others whom might not otherwise be able to get extra help...thank you for being a part of my quest!
When I took college algebra this is one of the first things my professor taught us. He was a good professor but did not explain the origin of where the h comes from, thanks for explaining
You're welcome @matt duran and thanks for watching and taking the time to "thank this teacher"!!!
nanananana dont know what id do without you. Thanks so much, I was so lost but now I found this.
+JXSHVA BAM!!!
Thanks for choosing my channel to like, sub and learn from!
Please take the time to tell all your friends about it and to do the same:D
If f(x)=2x-1, then f(x+h) is telling you to replace any x in the function with x+h, thus you have 2(x+h)-1. Thank you for choosing my video and I hope this clears up you question.
ProfRobBob, you're a really great person for this. Talk about giving back to the community. You make everything so easy to understand. Thank you very much for taking the time to make these videos.
You're welcome Emil...and THANK YOU for taking the time to acknowledge that and to share your appreciation! I hope you will continue to share this free resource with everyone and make sure they all take the time to like, subscribe, support the ads and keep spreading the word to help us keep growing...BAM!!!
Thank you so much. Just went over how to simplify this formula in my pre calc class, and it kills me when I don't know where something comes from. Great explanation.
Glad I could help...now please help us by liking, subbing, supporting the ads and sharing this free educational channel with everyone and remind them to do the same for all the free channels that they find helpful because that's how we grow and remain free...BAM!!!
This is one of the few videos that explains the IDEA behind the DQ and what it means, and that’s very helpful. Thank you!
You're welcome...thanks for taking the time to THANK the teacher and chose my channel to learn from...BAM!!!
Please like, sub and spread the word:D
I've had three separate professors try to teach me this over two years, and this video finally made me get one correct. Thank you.
I'd say that calls for a giant BAM!!!!
You're welcome and thanks for not giving up until you got it!...and found us:)
Thanks for subbing and don't forget to like and share this free resource thru social medias, with friends, parents, classmates and especially teachers so all students know where to find my 700+ videos and help:)
God bless you sir! I was struggling with this and you really explained it well. Not only did you show how to work it. You explained the background so it sticks!!!! Thank you sooooo much!!! Found this Feb 2019
Thanks for searching out the help...good thing math never goes out of style huh?!
Please sub and spread the word:D
I HAVE WATCHED SO MANY VIDEOS ON THIS AND IT SIMPLY WOULD NOT CLICK, THIS VIDEO COMPLETELY CLICKED. I CAN NOT BELIEVE HOW MUCH I WAS COMPLICATING IT. THANK YOU SO MUCH- FROM SOMEONE WHO ALMOST DROPPED CALCULUS.
Way to not give up and find the help you needed. With that kind of determination you should do very well this year! Here are my Calc vids organized by chapter, www.profrobbob.com/calculus
You're such a great teacher! I wish you were my math teacher for every math class that I took/will take. xD
+Jennolie THANKS...just like and subscribe and I can be your UA-cam teacher for 570 lessons...BAM!!!
Sat through class. Went to my professor's office hours. Stared at my homework for twenty minutes. Watched this video. NOW I get it. Thanks for helping me to understand that this difference quotient isn't the monster it looks like. It really is quite simple when you understand both the "how" and "why." Many thanks for taking time from your own day, to make my time worth a little more.
+Brocephus1994 BAM!!! That's AWESOME...thanks for taking the time to "thank" the teacher and to share your appreciation...and for not giving up after staring at your homework!
Thanks for subbing too and I hope you will share my channel and your experience with all your friends, classmates and teachers as you remind them to like, sub, support the ads, share thru social medias and with everyone they know to help these educational channel keep growing and remain free for everyone who is willing to invest the additional time in their future:D It makes a teacher proud:)
He didn't jump in :/.... that just threw off my whole day. I'm in shock.
+Martha DeGraffenried this was one of my early videos...if you keep watching you will find it becomes an all the time occurrence...BAM!!!
right? :D
You are an Excellent Teacher!! So clear and precise. I'm so glad I found your channel. I am in PreCal and can't afford a tutor. You made all the difference!
THANKS!!!
...and thanks for the compliments and the reminder why we continue to work so hard to keep this channel growing! Please like, sub, support the ads and share this free study resource with everyone...especially your teachers so ALL motivated students like you know where to find us...BAM!!!
Cant say thank you enough, there need to be more teachers like you in this world
You're welcome!
Please sub and share my passion for teaching with the rest of the world...start with your friends, classmates, teacher and thru your favorite social media so everyone knows where to find free math help...BAM!!!
Thank you for the nice feedback. When you want to evaluate/simplify f(x+h) write out the function with empty parentheses where there is an x, and then go back and put x+h in each of those ( ) and simplify. When the difference quotient asks for f(x)...well that is just the original function that was given so just write out the function. When you write out f(x), don't forget to wrap it parentheses because you need to distribute the - sign through that function.
I am going back to University. Which means I am watching all of your great videos to prepare for the classes.
I wish I had found this channel 10 years ago! Keep up the great work.
+David Leverett CONGRATS on going back to school and I'm glad I will be along for the preparation...please tell all your new classmates to like, subscribe and share these free educational channels with everyone to help us keep growing:D
(I've only been doing videos for 4 years anyway:)
i really dig how you explained WHAT the difference quotient is, instead of just telling us its some random formula, like my current precalc teacher. thanks. i will utilize you as a resource in the future.
THANKS for choosing my channel to watch and learn from foolishkl0wn !
I teach in full lessons which make the videos longer but thats why they make a fast-forward option right?! Please like, subscribe and share my channel with your friends, class and teachers as an additional study resource ~ and remind them to do the same to help us keep growing and helping others :D
Old, but gold. Thank you! Got an exam tomorrow and was fretting about this because I only half-understood it. Now I feel a little better!
Hope you passed that exam like BAM!!!...and after you do, please take the time to sub and share this free study resource with you class and teacher :)
10 years later THANK YOU!!!!
You're welcome...and thanks for watching and supporting!
Check out my THANK 10 year anniversary video and please keep spreading the word...BAM!!!
You are an amazing teacher. I love the way you explain things throughout your process. Thank you for explaining how the numerator is formed in the difference quotient from the algebra slope formula. My precalculus book did not show, nor explain the concept. Your students are so lucky to have you as a teacher! Thank you for sharing your expertise and teaching mastery with the world.
Thank you for the nice compliments Debbie! I hope you will continue to enjoy learning from Tarrou's Chalk Talk and if so you will like, subscribe and share my channel with the rest of the world:D
ProfRobBob Subscribe?? I guess I just exposed my lack of tech savvy. Please explain...
Debbie Bush
subscribing to a UA-cam channel helps to support their channel, makes it easier for you to find again, and you get a notification when new videos have been posted. Subscribers, views, duration videos are watched, likes, comments...etc are used by UA-cam to rank where videos are in the search results. Also the ads support the video producer (me), not just UA-cam.
Happy to help from so far away!...You're welcome and thank you for watching:)
Talk about a life saver just before finals.
Thank you for sharing this video!
You're welcome...and thanks for watching it!
Please SUBSCRIBE, Like and share if it helped you:D
you make math seem much more simple and actually treat your audience like they are intelligent people, VERY great! keep them up!
When in doubt, I always come here. Thanks! Seriously, you're awesome.
You have no idea how man teachers I asked back in highschool to do this for me. I am the type of person that NEEDS to know why things happen in a problem. This is exactly what I wish more teachers would do. Before watching this video I was confused on x+h section but now I see it is simply the input of the function....sometimes I just need to see it once to full grasp a true understanding. Thank you. Subscribing (and I rarely subscribe ever, you deserve it!).
tRilLot22 you're very welcome...and thanks for choosing, subbing and taking the time to share your appreciation and learning experience with us.
We are always glad to hear that these videos are making a difference and helping students who take the time to seek out the free help that is available.
Please keep sharing my channel and best of to you in the future:)
Studying for my math midterm and I was really about to cry because I had no idea what this formula was used for. Thank you so so much, it really is appreciated!
Happy to help..thanks for studying with Tarrou's Chalk Talk...please sub and share this free learning channel with your teacher too:D
...and then go pass that midterm like BAM!!!
Hello, Its the 2nd week of the summer semester and never seen this before, Ever! you made it easy to follow and I got the answer for my problem right the first try! Thank you!
You're welcome...I'd say that calls for a BAM!!!...lol
Thanks for studying and subbing and now that you have found us, please share this free resource with the rest of your summer semester class, especially your teacher so ALL current and future students know where to find free help:D (and remember to remind them to like, sub and share too:)
Yet another down right pleasant math tutorial.
BAM!!!
Thanks for subbing and supporting!
I am using this channel for review before my summer classes at UNC and I can't thank you enough for the awesome work. Also, I couldn't help but notice the chalk break at 5:14 only to fall right back on to the ledge of the chalkboard. CLUTCH.
The best way to understand Calculus ever!! In the world!
BAM!!!!
손일영 that's a pretty big statement, and I truly appreciate your support and appreciation! Thanks for watching, learning, liking and subbing too:)
This is great! I've just started calculus and my professor keeps referencing the difference quotient and saying it's important, but he hasn't really explained what it is very well. I finally get it! Thank you!
Oh man thank you so much. I just spent an hour doing practice problems online only to find out after checking my work that the online answers were wrong! Whoever made them forgot to distribute a -.
Anyway, I’m in college pre-calc doing these difference quotient problems and didn’t have a clue why they exist. Thank you so much for explaining the practical application, and a little about what comes next.
You're very welcome and thanks you for seeking outside help and choosing this channel. Please take the time to sub and share this free resource with everyone, especially your classmates and teacher!
Why can't all teachers explain things like this? most of the time its like: "YEAH YOU JUST DO THIS BECAUSE YOU JUST DO HAVE FUN". Thank you for actually explaining why these equations are written the way they are.
Thanks @Brandon P for the appreciation of my teaching style...many do not agree and are looking for a 15 minute video but I chose to build this channel with full lessons and a fast forward button:) Thank you too for subbing...we hope you will take the time to share this free channel thru social medias, with friends, parents, classmates, teachers and anyone learning from home now to help us keep growing and helping others in these challenging times...BAM!!!
I am glad I could help. Thanks for watching:)
Liked that you used time to explain the intuition behind the math. Others just make an example of how to find it given a certain defined f(x).
Most of my videos are full lessons which mimics my teaching style in the classroom. Thanks for choosing my channel to watch & learn from!
Really helpful! I have a test on Monday and this was confusing to me until I watched this video! Thank you so much!!
+Sam Youngblood you're welcome and thanks for studying and subbing to my channel...now go pass that test like BAM!!!
You're welcome...Thanks for choosing my channel to watch and learn from!
Thank you for your time and patience! It's becoming clear!
The more you watch...the more you learn A Lauris ...good to see you watching more already:)
You are so welcome...I'm glad to hear that you are un-stuck now:)...and thanks for watching and subscribing!
Rob Bob u r awesome! Your slight "over explaining", is really useful for reinforcement. I know it takes additional time, but what might come intuitively to some, when skipped, becomes a road block to advancement for others
THANKS for appreciating my efforts and teaching style!
Please share :D
You're welcome:) I'm glad to see you are still watching and learning and preparing for those exams!
This is super detailed I love it. So hard to find someone actually explain formulas well on youtube.
Thanks for tuning in!
Please like, sub and share if you continue to find this free educational channel helpful:D
You know you are a math king when you smash your chalk three times in one video...
But seriously, good video, great help!
So I ask...what would Elvis do?!...lol
this helped me so much I understood more from this video than a year of high school math
BAM!!!
Sounds like the perfect time to share this channel with your class and especially your teacher right after you like, and subscribe:)
I appreciated your passion and the way you delivered the lessons!!
+Steffi Bermudes thanks for tuning in!
Great video!!! this ProfRobBob Rocks!!
THANKS Eder Santos !
I just want you to know that I spend my weekends watching your videos. Thank you!
It's nice to know I have company...that's usually the only time I have to produce new videos! Good thing I have such a supportive and understanding wife of 20 years:) Thanks for supporting and subscribing too...I promise all the extra work will pay off!!!
If you pause it on 0:18, he stands like a "Sir". Great explanation. Thanks.
This is only my first video of yours that I have viewed, and I must say you are an amazing teacher! I really hope you continue creating these tutorials/lessons in the future. You get the idea across, you're descriptive, and you add a bit of humor. After sending this comment, I will be liking this video and subscribing to your channel. I really wish that I was able to spread the word of such an amazing channel; however, I am in an eighth grade (U.S.) Algebra 1 class (highest course offered in my grade), and as you may expect, I am the only person that I know that enjoys studying Geometry to Calculus. So once again, thank you.
Jacob Adamczyk sorry for the delayed reply:(THANK YOU for taking the time to share such a nice compliment and for liking and subbing to my channel. You're teachers must love having such a prepared student:)
I hope you will continue to enjoy my lessons thru your upcoming math courses. You should try sharing with some of your friends and classmates...maybe you can help them see that math does not always have to be boring to learn...BAM!!!
I try to "teach" how to find the solution so you understand where the solution comes from. Thank you for watching and commenting on another video...that tells me you are watching more than one...plus, thank you for subscribing too. Please share with your friends, my growth is thru the support of my subscribers....so I'll keep them up as long as you keep supporting and sharing the resources:D...thanks.
You're one of the excellent math teacher!!!!
mark jackson THANK YOU!
I finally get it, thank you SO much. You're an amazing teacher
You're welcome so much!
THANKS for watching and subbing.
THANK YOU!, for not just showing how to do the problem, but EXPLAINING the how, what and why of the difference quotient. Usually when I know the why, it makes memorizing formulas moot because I actually know what's going on.
And THANK YOU señor shaman for choosing Tarrou's Chalk Talk to watch and subscribe to and for taking the time to share your appreciation! I decided to record my videos as full lessons originally to help one of my classroom students who was going to be missing some class time and the response was so great that I just continued as my channel has continued to groW! Please continue to share your experience with others and spread the word about my channel and help me continue to groW and help others...BAM!!!
Thank you very much. You made so clear than that of my teacher.
You're welcome and thank you for taking the time to seek outside help, subbing and studying! Sounds like the perfect time to share this free study resource with your class and especially your teacher:D
Professor RobBob, thank you once again for a powerful lecture/video on the Difference Quotient in Precalculus. Students will encounter this material in Calculus One.
Of course. Thank you very much for the videos and the comment responses.
WOW...it is just awesome. Thank you for the upload sir!
You're welcome and THANK YOU for watching!
Please sub and share with everyone...BAM!!!
And thank you for subscribing and working so hard over the summer:) You keep watching and I'll keep answering those comments the best I can:D
Your teaching amazes me
Thanks for choosing #ProfRobBob to subscribe to and learn from Mike Hillyer ...I hope you continue to be amazed! And then you will tell all your friends to Like me on Facebook, watch, like, subscribe and share my channel with all their friends and so on and so on until I get a million subscribers...BAM!!!
This saved my life thanks
You're welcome rjamesfinn2 ...now don't forget to Support this channel, Like, SUBSCRIBE and tell all your friends/class and teachers to watch and do the same:D
Wow. Thank you for this very helpful tutorial.
You're welcome and thanks for choosing this channel;l to study with!
Please sub and share this channel with everyone...BAM!!!
And THANK YOU for watching, liking and supporting by subscribing! Please share my channel with your friends and classmates and help me continue to groW:)
Thank you for explaining so simply what my textbook, professor, and homework examples all couldn't explain.
...and thank you for taking the time to study with Tarrou's Chalk Talk!
We hope you'll take the time to like, subscribe, support the ads and share this channel with everyone if you continue to find it helpful:D
Thanks for sharing that GREAT news, CONGRATULATIONS!!! (does that put me in superhero status now?!..lol)
And remember...we did it "together"...you were the one who sought out the extra help!
Thank you for really teaching and explaining complex math so well:)
+kelly williams you are so welcome and THANKS for choosing this channel to learn from and sub to!
Please spread the word:D
Thanks...and THANKS for subscribing and supporting:)
You're welcome. Happy that I could help!...now you can help me by subscribing and sharing my channel with your friends:D
I will keep making videos as long as you keep watching and learning!
I shall! I ended up taking on a precalc exam today, so I'll be watching a lot more of your videos so I can retake t later in January, and probably continue watching when I move on to calc next semster!
You're welcome...and YOU ROCK for liking my video and choosing my channel to learn from:)
Now Closed Captioned #math
...or I can say with a line the slope is constant regardless of which two points you use to find slope. Thank you for watching and your support!
Glad to hear this video could clear thing up for you...THANKS Werner I really appreciate the support of liking and subscribing too! Be sure to tell all your friends where to find me and to do the same!
Thank you, Sir! May God bless people like you! I wish my professor would teach us like that.
This was on an exam but not taught in class. Awesome. Thanks for this video
With "fancy way of writing slope you" the entire lesson became clear, thanks
Now it makes complete sense.
BAM!!! TheMorfin2011
my current teacher skipped the whole idea behind the diff quotient. She just gave it to us w/o any explanation. I had to teach it to myself....
oh man you saved me!! I think i'll be using your channel to study for my pre-cal final. we only have one week after thanksgiving break to study and im a very image-based learner. also you have gorgeous handwriting :) thank you!!
You're welcome Layla…and thanks for supporting, watching, commenting and subscribing! Now "go do your homework" and pass that final with the "A" you deserve!
Thank you so much for posting this!!!!
You're welcome and thanks for studying and subbing...please spread the word:D
Thank you for this great lesson. Best explanation I've heard yet of what seems like a foreign concept when presented to someone although after learning this its so obvious and simple its hilarious to remember my initial struggle and reaction to seeing this equation.
you're welcome, I would cll that a "BAM!!! moment:)... and thanks for choosing my channel to study with and sub to!
Please tell all your friends and classmates to watch and do the same:D
Definitely will! Thanks again.
:)
I love you too for watching and supporting my channel. Sorry it took a few days to comment:) My teaching job is keeping me extremely busy this year.
The Difference Quotient is my favorite part of Calculus 1 because it's so easy!
Keep enjoying math ***** !
Thank you and yes I have one Calculus final and I am done! Next stop is Calculus 2: Integration and I would like to thank you for your awesome videos cuz they were very helpful to me.
***** sounds like you are a strong, motivated math student.
Thanks for learning from #ProfRobBob and I hope you'll SUBSCRIBE and share my channel with your friends and classmates:D
thank you again kind sir.
because of you i got a 95% on my first pre calc test ;)
This video is ancient, but you just saved my pre-cal grade. My prof doesn’t explain *why* things are what they are, and I need that explanation to actually understand the material.
Then that must make me prehistoric...lol
Yes, the was one of me first videos and somehow I'm still making new ones as the math I teach gets more advanced. New subscribers and spreading the word help us keep growing too!
Thanks for seeking outside help and I'm glad I could help
Because for my first example y=2x-1 is a linear function, a line, which is going to have a constant slope of two at any value within its domain...x.
Thanks sir, u r amazing!!!!, thank u so much again
...and THANK YOU for watching, liking and subbing to this free channel:)
Please share with everyone and tell them to do the same...keep spreading the word so we can keep growing and helping students for free:D
Problem solving, distribution technique, sound logical process, thank you :D
BAM!!!
You're welcome...please remember to sub and share this free channel with everyone:D
Thank you so much. This is the only video I could find that actually explains the different quotient.
You are simple and the best!!!
Thank you so much for your dedication!!!
And "Thanks" for liking, learning and subbing to this channel !
Please spread the word and tell everyone to watch and do the same...BAM!!!
nice video i am a a sophomore in pre-cal and this cleared it up thanks
You're welcome Jakeob Arevalo ...please SUBSCRIBE and share my channel with everyone:D
Thanks for watching and liking!
alittle awkward at times, but extremely effective. Good work, learned in 15 mins what it took my professor to teach me in like 6 hours of class time.
Thanks for watching...this was one of my first videos..I've done almost 600 more since this one and I promise it gets better...BAM!!!
And Thanks for watching!
Watch Slope of a Tangent Line Derivative at a Point. I hope you do great on your test!
Man, you really are a great teacher. Thanks for all of your help!
Thank you Matt! I hope you continue to enjoy your learning experience from Tarrou's Chalk Talk:)…and then tell all your friends to watch and SUBSCRIBE too!!!
Rob Tarrou and Jerry Fowler are my favorite math teachers. To paraphrase Fleetwood Mac, you make learnin' fun.
That's what I like to hear Murray Melander ...math and fun in the same comment BAM!!!
Thanks for watching, liking, learning and subbing and I hope you are telling all your friends to watch and do the same:D
ProfRobBob I watch all the the time. I'm back in college in electronics and math courses. So your videos are the perfect adjunct to class time.
Murray Melander AWESOME...then it sounds like I have the potential for a lot of new subscribers when you start sharing my channel with the rest of your classmates and teachers...BAM!!!
I am so glad that you told me where ''h'' came from. I WAS GETTING VERY FRUSTRATED BECAUSE I COULDN'T FIND A YOU TUBE VIDEO THAT EXPLAINED THAT PART. :D
BAM!!!
Thanks for choosing #ProfRobBob to teach you and I hope you will return the next time you need help and avoid all that "frustration" Christopher Rice :)
You are an amazing professor!!! You have an obvious talent in knowing exactly how to take your knowledge in your mind and pour it right into the minds of your viewers! I was struggling with understanding this concept and you cleared it up in 15 mins! Thank you so much for volunteering your time! I feel so much more confident to succeed now! My sister highly recommended your videos. I've subscribed and will watch all your videos!
Hey Brenda...In case you missed it, I replied on your channel page because for some reason I was not able to reply directly from this comment:(
Keep watching, sharing and reminding your friends to SUBSCRIBE and support free educational channel like mine...educators work very hard to keep these channels free and available for others to learn from:) THANK YOU and your sister for watching and taking the time to "thank the teacher"!