Sketching the Derivative of a Function

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Buy my book!: '1001 Calculus Problems for Dummies' - you can get it on my website: patrickjmt.com/
Sketching the Derivative of a Function - In this video, I sketch the derivative of two different functions. That is, I give the graph of y = f(x), and do a rough sketch of the graph f ' (x).
For more free math videos, visit PatrickJMT.com

Пікірлер: 508

  • @henryle4407
    @henryle44078 жыл бұрын

    The moment when you realize that learning on youtube is more effective than learning from your actual teacher at school Thank you for saving my life!

  • @mikegarcia2279

    @mikegarcia2279

    5 жыл бұрын

    Agreed. Bless this video

  • @APSEAPSE

    @APSEAPSE

    5 жыл бұрын

    So true

  • @brymetheous2387

    @brymetheous2387

    4 жыл бұрын

    Yeah agreed, it's like my math professor just teaches me what to look up

  • @juliablanchard4994
    @juliablanchard49944 жыл бұрын

    10 years later this man still saving us

  • @gautamdatta8194

    @gautamdatta8194

    4 жыл бұрын

    11 years now :D

  • @bobjoe164

    @bobjoe164

    4 жыл бұрын

    like for real man God bless

  • @vigyatpandey1943

    @vigyatpandey1943

    4 жыл бұрын

    FOR REAL

  • @jordancoats525

    @jordancoats525

    3 жыл бұрын

    Fax

  • @kendyllb7400

    @kendyllb7400

    3 жыл бұрын

    make it twelve

  • @ST5S5
    @ST5S510 жыл бұрын

    You taught this to me in 15 minutes better than my math teacher could in an hour. Thank you!

  • @sebon11

    @sebon11

    5 жыл бұрын

    Same here

  • @vpkasar7858

    @vpkasar7858

    Жыл бұрын

    yall are old

  • @user-mk3yo6wo2h
    @user-mk3yo6wo2h9 жыл бұрын

    I want to point out in the first example, the graph is a cubic function. We can arbitrarily say x^3. Using some basic calculus rules, we can say the derivative of x^3 is 3x^2. 3x^2 is a parabola. That can help you identify which graph is the derivative. =)

  • @StephenRayner
    @StephenRayner10 жыл бұрын

    At around 5:38 I got slightly confused for a few seconds. To me you had your pen pointing down (i.e. negative) but you was saying it was getting more posative. But then I remembered we consider the direction from -x to x. so if the line is going from y = -5 to y = 5 from left ro right it is increasing and so is posative. If you consider the other way then you have negative but we consider from left to right. Hope this helps others who may have been slightly confused for a second.

  • @LiOnHeLl-kc8vy

    @LiOnHeLl-kc8vy

    5 жыл бұрын

    yea i was so confused. Thanks for the heads up.

  • @alexmorgan4220

    @alexmorgan4220

    4 жыл бұрын

    Thanks >3

  • @gabrielamendoza4489

    @gabrielamendoza4489

    4 жыл бұрын

    😁

  • @SuperKilltacular1
    @SuperKilltacular110 жыл бұрын

    pretty sad when your instructor sucks at teaching and you have to come here just to learn how to graph a derivative...

  • @fyzy123
    @fyzy1238 жыл бұрын

    You are so much more helpful than my own professor. Can I pay you instead of her like seriously the class I'm taking is bullshit

  • @patrickjmt

    @patrickjmt

    8 жыл бұрын

    Works for me! Seriously though, sorry your class sucks!

  • @caseysheehan3182

    @caseysheehan3182

    8 жыл бұрын

    +patrickJMT But seriously you just helped my roommate and I with a quiz, TAKE MY MONEY

  • @trixiefortich3142
    @trixiefortich31425 жыл бұрын

    "sorry for my bad graph" wait till you see my graphs....

  • @patrickjmt
    @patrickjmt15 жыл бұрын

    that is a nice turn-around grade-wise : ) glad the vids helped

  • @Dean444ful
    @Dean444ful7 жыл бұрын

    Can you be my calculus teacher?

  • @xueyiwang9738

    @xueyiwang9738

    6 жыл бұрын

    mitch-bittens 😂

  • @mangalamokashi9908

    @mangalamokashi9908

    4 жыл бұрын

    mitch-bittens he already is😁

  • @SammyWinFL
    @SammyWinFL13 жыл бұрын

    @patrickJMT A great teacher like yourself will surely be repaid for their good deeds as a person in one way or another! I'm studying for the PCAT exam and this helped so much. Thank you Patrick

  • @mirandashirley4697
    @mirandashirley469710 жыл бұрын

    Thank you so much! My teacher flies through our calc lessons so this helps TONS. I really appreciate it.

  • @rotate58
    @rotate5814 жыл бұрын

    I can't thank you enough, your fantastic explanation and teaching method helped me to understand what close to three hours of confusing instruction with my own teacher could not. Thank you!

  • @patrickjmt
    @patrickjmt15 жыл бұрын

    ya! that is probably possible! i will try to make one later today if i remember and dont get lazy! (gonna be a beautiful day today... dont wanna be inside making math videos!!) : )

  • @valkyrie034
    @valkyrie03413 жыл бұрын

    Thanks for the help, keep the videos rolling. First semester Calculus, and was having trouble with graphing them- couldn't wrap my brain around it, but I've got it now!

  • @uriellopez6529
    @uriellopez65297 жыл бұрын

    It's been years since I've been in school and I'm returning in a couple of weeks and your videos have made me confident in my math skills once more!!! Thank you so much!!!

  • @rahrahritaa
    @rahrahritaa12 жыл бұрын

    calc final in 2 hours! this is a great review

  • @fe.rya.lazeem

    @fe.rya.lazeem

    2 жыл бұрын

    so how was the final lol

  • @randomstuff940

    @randomstuff940

    2 жыл бұрын

    @@fe.rya.lazeem LMFAO

  • @ilikedetectives
    @ilikedetectives13 жыл бұрын

    Thank you so much!!! My teacher skipped in class this part and now I'm having trouble with doing the hw. You just saved my life!!!!

  • @Countrycon
    @Countrycon13 жыл бұрын

    You are hands down better than any math teacher I've ever had.

  • @patrickjmt
    @patrickjmt15 жыл бұрын

    thats true... if i called it the 'step function' i spoke incorrectly! it does clearly 'jump around' though

  • @memirandawong
    @memirandawong10 жыл бұрын

    Well, you have rendered my calculus book astonishingly useless with your videos! That's okay. The only thing I still need it for is the assigned HW problems!

  • @TheWarfare07
    @TheWarfare077 жыл бұрын

    this is great. i learned so much more in 15 mins than being in class for 2 damn hours. thanks

  • @mattreese
    @mattreese14 жыл бұрын

    I've watched many of your videos, they are a huge help. Thanks for breaking it down into lemans terms for me.

  • @dannyzuko1850
    @dannyzuko185010 жыл бұрын

    This probably won't mean a lot with the countless 'thank you's you receive everyday, but I seriously want to thank you. This is EXTREMELY helpful. Bless YOU!

  • @joshuahurtado882
    @joshuahurtado8825 жыл бұрын

    dude, well done. I finally understand this concept, my instructor tweakinggggggg.

  • @coyotes2012
    @coyotes201211 жыл бұрын

    Your videos always give me a good refresh for my college calculus class. Thank you VERY much for these videos. Helpful and to the point

  • @xxpunkxxgirl
    @xxpunkxxgirl12 жыл бұрын

    Awesome!! We're doing this in calc now, and you taught me better in 15 mins than my teacher did in a whole week.

  • @hartake6667
    @hartake66679 жыл бұрын

    Boss! With just the first 5 minutes I've been able to make deductions to answer 5 questions on the assignment correctly.

  • @puckSHOCK
    @puckSHOCK13 жыл бұрын

    I started Calculus a month ago, in that time, I think I've watched a majority of your calculus videos. Thank you for saving me :)

  • @patrickjmt
    @patrickjmt12 жыл бұрын

    @MrAznSoldier thanks for taking time to watch my videos : )

  • @PRDZ110
    @PRDZ1102 ай бұрын

    15 years later and ur still the goat man !

  • @EmilyDeibert
    @EmilyDeibert13 жыл бұрын

    You probably just saved my life for my calc test tomorrow! Keep up the good work!

  • @patrickjmt
    @patrickjmt12 жыл бұрын

    @PSliveNlove happy to help!

  • @rzehrahayder7788
    @rzehrahayder77885 жыл бұрын

    honestly thank you, seriously needed this

  • @1MrShiny
    @1MrShiny9 жыл бұрын

    you taught me in 10 minutes, what my textbook couldn't teach me in 2 weeks. You are a miracle, i suddenly feel more confident about my upcoming test. Thanks!

  • @patrickjmt
    @patrickjmt11 жыл бұрын

    glad i could help you out :)

  • @elyazzoo
    @elyazzoo12 жыл бұрын

    hey i really appreciate this my teacher doesn't really fit my learning style at all so you are literally getting me through calculus

  • @VinUnleaded182
    @VinUnleaded18212 жыл бұрын

    thank you so much. spent hours to wrap my head around this and your video cleared this up a lot

  • @delahkful
    @delahkful7 жыл бұрын

    i just love you so much, i've always had miss understanding on this.

  • @scribbledheartz
    @scribbledheartz11 жыл бұрын

    This made a hug impact on my graphing ability. In my calc book there's questions but no explanation on how to go about graphing derivatives of a function. So thank you!! :)

  • @mf7114
    @mf711411 жыл бұрын

    Thank you so much! I am in calc my freshman year of college and even though I go into office hours and such, I had NO idea what was going on. Thanks for explaining it in plain english and not some fancy math lingo :). You're awesome!

  • @lizzyjane1361
    @lizzyjane136110 жыл бұрын

    THANK YOU! 6 days before my mocks and I was freaking out about this. You're my hero :)

  • @patrickjmt
    @patrickjmt13 жыл бұрын

    @readingMUNKY glad you like the vids; congrats on the first test!!

  • @RyanLawrence1
    @RyanLawrence113 жыл бұрын

    awesome set of videos. These videos are perfect for helping review for a test. Thanks for making these!!

  • @Marina-zn8ip
    @Marina-zn8ip8 жыл бұрын

    This was so helpful!! Have a calculus exam next hour and this video has been way more productive than anything my teacher ever said.

  • @rachelmgosse2195
    @rachelmgosse21954 жыл бұрын

    oml a king thank you. you helped me understand and now it all clicks!!!

  • @madelyndriver1213
    @madelyndriver121310 жыл бұрын

    Thanks for the lesson. I got a high fever the second week of classes and am trying to teach myself Calc before classes start again on Tuesday. This helped a bunch!

  • @Beauty_by_Summer
    @Beauty_by_Summer11 жыл бұрын

    omg sir u dont know how much youve helped me! im a senior in high school and im taking AP calc, the teacher never explains stuff! but u made it much more clear. thank u!

  • @0bsessionist
    @0bsessionist13 жыл бұрын

    You're better than my calculus professor! Thank you so much!! You're saving my grade!

  • @mintbreakart
    @mintbreakart11 жыл бұрын

    THANK YOU SO MUCH! This is the only bit I didn't understand. And I got it immediately.

  • @audaciousifti
    @audaciousifti4 жыл бұрын

    Thanks for the help, you explained this really fast and easy and helped me with my homework and test study.

  • @patrickjmt
    @patrickjmt12 жыл бұрын

    glad i could help you :)

  • @patrickjmt
    @patrickjmt14 жыл бұрын

    @rosepetals1002 u r very welcome

  • @CL-lr9wh
    @CL-lr9wh9 жыл бұрын

    I spent three semester on calculus and didn't know how to sketch this. And you helped me just in a few minutes. Thanks!!!

  • @safar127
    @safar12712 жыл бұрын

    I WAS SO LOST BUT U MADE ME FIND MY WAY AGAIN THANKS!!!

  • @patrickjmt
    @patrickjmt11 жыл бұрын

    because the slopes of the tangent lines are constant over those intervals

  • @doctacool312
    @doctacool3129 жыл бұрын

    watched a ton of videos and this is the first one that helped me understand how to imagine the derivative properly, thank you

  • @shannonsullivan3193
    @shannonsullivan319310 жыл бұрын

    So unbelievably helpful! Thank you so much!

  • @macallancruff2828
    @macallancruff28289 жыл бұрын

    I have a crazy math teacher who looked at me like I was crazy when I asked her what the heck she was doing. Thank you so much for clarifying! Keep being awesome!

  • @adamdebesai
    @adamdebesai10 жыл бұрын

    With your explanation and teaching, who wouldn't get this? Great video!!!

  • @carmelamorano6296
    @carmelamorano62963 жыл бұрын

    It’s 2020 and this is still helping people

  • @thomasmorris9180
    @thomasmorris91806 жыл бұрын

    Thanks v. much for this - makes sense. One small point though, on your first parabola graph, should the negative parabola for the derivative not slowly decrease first before rapidly decrease to the arbitrary negative five maximum?

  • @nobazter
    @nobazter12 жыл бұрын

    love you man your video wins!! learned the best from you

  • @oris314
    @oris31413 жыл бұрын

    Thanks bunch! i have calculus homework on graphing derivatives with only having the graph of f(x) and didn't understand it at all. now i can actually get my homework done!

  • @omarmartinez399
    @omarmartinez3999 жыл бұрын

    dude, you explain this with such great clarity thank you!

  • @keithbt430888
    @keithbt43088813 жыл бұрын

    this makes graphing derivatives seem too easy, i hope the school you teach at really appreciates you. :)

  • @fahimshahriar224
    @fahimshahriar2242 жыл бұрын

    ooh man . i was literally looking for this kinda explanation . thanks

  • @colinwhitlock5148
    @colinwhitlock51484 жыл бұрын

    I'm just confused as to how we figure out the minimum y value of f'(x) when we aren't actually given any values on the graph

  • @LeonardNdegwazugzwang
    @LeonardNdegwazugzwang11 жыл бұрын

    You have THE best vids in calculus THANKS

  • @CiarasDream
    @CiarasDream10 жыл бұрын

    I have one question! For the second root, above the minimum of the function, you brought the graph up because it was less negative than the tangent where m was -5. What I don't understand is that on the function it was LESS negative but still negative, and then on the derivative it went to positive... Shouldn't the continuation of the derivative have been just a bit less steep in its gradient rather than positive? I definitely understand this better, thank you !!

  • @shahadmerani3116
    @shahadmerani3116 Жыл бұрын

    the graph I’ve been struggling with for 3 days..u basically saved my life lol 💀

  • @lizbizwiz1238
    @lizbizwiz12386 жыл бұрын

    Dude, I have a Derivative test tomorrow and you are a lifesaver!

  • @anilsharma-ev2my
    @anilsharma-ev2my4 жыл бұрын

    How we find length of curve between it's solution so we got some more confirm behavior?

  • @DeJayHank
    @DeJayHank15 жыл бұрын

    failed my first exam. 2 months later i had another chance. used your tutorials for 2 days and got top grade. thanks alot mate =)

  • @sabihhaider4823
    @sabihhaider48233 жыл бұрын

    Thank you for an awesome explanation, to this topic

  • @teddybears23458
    @teddybears2345810 жыл бұрын

    Thank you very much for the helpful video; it helped me understand things more clearly. But I'm confused-I thought that increasing/decreasing was decided from left side of the graph to the right-which means that the red part of the graph on the left of the y-axis is technically decreasing, rather than the way its supposed to be increasing. Is that right?

  • @patrickjmt
    @patrickjmt12 жыл бұрын

    @Xx0Mystic0xX i will also post it as a video response in the comment section

  • @sakaklovas
    @sakaklovas14 жыл бұрын

    Um... you just taught me in 15 minutes what I was struggling to learn for days...thank you.

  • @MoonMoon-bj9jr
    @MoonMoon-bj9jr3 жыл бұрын

    this man still coming clutch after 11 years

  • @richardparker123
    @richardparker12310 жыл бұрын

    So the y-coordinate of a point on a tangent line is equal to the slope of that point?

  • @XgtkidX
    @XgtkidX14 жыл бұрын

    thanks so much i couldnt understand th book at all. you helped so much!

  • @DannyLinux
    @DannyLinux12 жыл бұрын

    @bwill115 its because the tangent line is pointing towards the positive Y coordinate as it goes from -infinity to +infinity! (:

  • @juliankashama1279
    @juliankashama12794 жыл бұрын

    Hey Patrick! Thank you for helping me with my engineering degree. I feel like I know You! We spent long math nights together. 🤣🤣Graduated last year. Just want to saying thank you. You have a God given gift! You helped me out big time!! Thank you. Writing from Botswana! Much love!

  • @patrickjmt

    @patrickjmt

    4 жыл бұрын

    Happy to help!

  • @EGabrielFulton
    @EGabrielFulton10 жыл бұрын

    You my friend, deserve a medal.

  • @lakshyachopra_
    @lakshyachopra_2 жыл бұрын

    This video is really helpful, thanks a lot!

  • @MrCaRTom
    @MrCaRTom14 жыл бұрын

    i have a math test today in a few hours, been watching your videos for the stuff i had trouble with and since i went over them so much, that's the stuff i feel better about :) i hope i do good on the test..

  • @LilbabyonYT

    @LilbabyonYT

    Жыл бұрын

    I hope you aced that test. How’s life?

  • @OverlyCuriousEngineer
    @OverlyCuriousEngineer10 жыл бұрын

    You sir, are the best tutuor to ever step on the face of the earth. Hats off!

  • @juliendark4208
    @juliendark42087 жыл бұрын

    Just ordered your book!

  • @patrickjmt

    @patrickjmt

    7 жыл бұрын

    I hope it helps ;)

  • @kingsley182
    @kingsley18212 жыл бұрын

    Desperate attempts have led me to the internet. I found your video. THANK GOD. I AM GOING TO ACE THIS DERIVATIVE GRAPH IN MY MATHEMATICS EXAMINATION TOMORROW. THANK YOU.

  • @ceemihail
    @ceemihail6 жыл бұрын

    I've been having one of those day for 3 weeks now trying to get calculus, thx for the videos.

  • @patrickjmt
    @patrickjmt14 жыл бұрын

    @rotate58 glad i was able to help make some sense of it. perhaps your instructor helped 'warm you up ' though : )

  • @animemewmew7
    @animemewmew79 жыл бұрын

    Thank you Patrick :) You are helping me to understand and relearn (better, this time) calculus before my AP exam next Tuesday.

  • @mblackops2

    @mblackops2

    5 жыл бұрын

    catsithkellas I'm taking AP Calc rn. I'm thinking about dropping out. Is it worth it? School has started for like a month now and I have a D in the class. I got an F on my quiz and on my test.

  • @zaidalsayes
    @zaidalsayes10 жыл бұрын

    please teacher can u explain me how why did u graph holes in the derivative on cusps and u didn't graph any hole in the previous example even there was two cusps ,, thnx

  • @PossumPog64
    @PossumPog64 Жыл бұрын

    2023 and this man is still saving the lives of all STEM majors

  • @eatyoriceful
    @eatyoriceful12 жыл бұрын

    AMAZING video thank you soooo much i was about to give up on this curve sketching crap TT-TT but this video explains it very clearly

  • @yuhoseok47
    @yuhoseok478 жыл бұрын

    you are such an awesome teacher. Thank you I really appreciate

  • @calebweidenbach
    @calebweidenbach9 жыл бұрын

    on the second example when you plotted the first point you said that the height should be at negative one. why is that? is it because that is based on the slope?

  • @patrickjmt
    @patrickjmt13 жыл бұрын

    @Ilikeroots ops, thanks for posting this, sorry it took e 3 months to notice. it is gone now : )

  • @syn586
    @syn5867 жыл бұрын

    You were really helpful man. Really.Thankyou. And no your sketching isn't that bad.

  • @GoChaca
    @GoChaca7 жыл бұрын

    You are the reason I am passing Calc. thank you so so much!