Rolle's Theorem to Prove Exactly one root for Cubic Function AP Calculus

[@syremusic_]

Fantastic video. Clearly explained, no fuss. Wishing more teachers were like you. Thank you.

[@MathematicsTutor]

Thanks

[@DanT-iu6oc]

Who will win? A $200 textbook written by a multimillionaire Stanford Professor (James Stewart), or an 8 minute video on KZbin? ridiculous

[@MathematicsTutor]

not we

[@thandiiid1300]

Literally😒 I've had that big textbook in front of me for the past hour and this video helped me in less than 10 minutes.

[@DanT-iu6oc]

@@thandiiid1300 TRUTH!!

[@andynonymous6769]

@@MathematicsTutor You did a great job of explaining

[@oliviawoloshyn5824]

Easy to understand and and he's got a really soothing voice. Thanks, thumbs up :)

[@myra8695]

thank you, this is the only time ive understood rolle's theorem

[@csaasd688]

Absolute bloody legend, Thank you so much

[@shrithanosmaharaj8679]

Blaady

[@dinithisahanika7823]

Just wow! Everything explained within 8 minutes ..love from sri lanka ,❤❤

[@MathematicsTutor]

Thanks for appreciation. Here is another related video: kzbin.info/www/bejne/g6ulioOVr7iMhKs All the Best!

[@gauranshbaveja335]

Thank you so much. I was stuck so badly on this but now its so much more clear!!

[@sabelophilani6973]

6 years later and still going strong❤🔥

[@MB-sk6oc]

Thanks alot !!! i was stuck on assumption part, but now its all clear.

[@MathematicsTutor]

It is tricky. Glad it made sense to you. Thanks for appreciation.

[@elduderino7456]

Just one note that 3x^2 is not always positive it is 0 when x =0, f'(x) is always positive because of the +1, other than great and clear explanation thank you.

[@christophermontoya5526]

Thanks for this. It's true my math teacher has shown us this in class, but I can't rewind and watch his lectures over and over. This I can watch repeatedly.

[@jaivardhannani4612]

Excellent lecture. I clarified my doubt by u after asking my sirs....

[@subhradeka690]

nice precise and to the point explanation

[@scapedrag7893]

Thank you so much. Your video really helped me alot. Please keep posting

[@MathematicsTutor]

Thanks a lot. Feel free to post questions. My e-mail: [e-mail] Best

[@sebastiansorondo4440]

One of the best examples thank you!

[@danielhewlett2395]

Thank you very much. Concise, clear teaching, well done.

[@megancower1884]

Beautiful explanation. Other than the comma that makes f(a)=f(b) look like f(a)=f(prime)(b) At 5:07

[@Ceecee384]

How would you do this question if the equation was X^3 - 15x + C = 0?

[@khalidabdulazizhusseinalkh1249]

anil u r the best

[@liamedgecombe9005]

Thank you so much!

[@MrJbismyidol]

amazing thank you so much.

[@MathematicsTutor]

Thanks for appreciation

[@SachinKumar-hz7nq]

No need of Rolles theorem because it is increasing function on R

[@ansonthai4709]

excellent video

[@John-thinks]

Thank you. Helped a lot. I finally understand this.

[@samuelpak669]

Since when did the AP Calc exam start asking proofs?

[@shalinimaurya9297]

very helpful video,sir

[@MathematicsTutor]

Thanks. Related question: kzbin.info/www/bejne/g6ulioOVr7iMhKs

[@jaisinghsaharan7846]

Sir please upload advance level questions on mean value theorem

[@irinmaryissac4364]

Thank you so much sir

[@joeoliver5276]

thanks helped so much!

[@fayaznashibe5490]

Tnx a lot sir

[@munaifaarif9352]

Thanks for your video sir! Is it possible if you could just give similar questions for practice or even suggest a book to practice further similar problems?!

[@jamka5]

tuff ahh

[@MathematicsTutor]

No worries. Playlist for you: kzbin.info/www/bejne/aZq5mp5_hplobNk

[@keltonlepak7029]

What kind of pen is that?

[@baturalpk.456]

finally I got it, thanks for it

[@MathematicsTutor]

Thanks. All the Best!

[@AtebitAcorn]

Yes it did help

[@אורבןדודאוחיון]

Thank you

[@shjkesnc3502]

@AnilKumar what if it has 3 real roots?

[@emz5439]

what kind of pens do you use?

[@cjdacumos1166]

i liked how you paused for several seconds because u'r not sure about the spelling lol anyways good content dude

[@platonic5085]

Nice pens

[@mehrunnisa2044]

Hello Sir! Your work is greatly appreciated. Would you please tell me that how to prove ( All real cubic polynomials have atleast one x-intercept )

[@Jacob-sj1jp]

any cubic will approach infinity and -infinity for all cubic polynomials this it must cross the x axis as the y domain is [-infinity, infinity]

[@mehrunnisa2044]

Thank you Sir!

[@AC0_0]

T H A N K Y O U

[@MathematicsTutor]

Thanks. Have a Great Day!

[@leonardotshirt]

Profe crack😎

[@ITSPETETHEBEAST97]

Qhat pens do you use they look amazing or can anyone answer

[@MathematicsTutor]

Pens are shown in this video: kzbin.info/www/bejne/mZyQfohuhdKqsNU Thanks

[@va11bhav_rana]

Lol, pens are more interesting then maths

[@diptirani6524]

How it is shown that it is diffrentiable

[@tb2748]

Is there a way to algebraically find this root? Rational root theorem/test doesn't seem to be helpful here (unless if I am wrong).

[@MathematicsTutor]

Graphing Calculator, or Newtons method video: kzbin.info/www/bejne/g6ulioOVr7iMhKs Thanks

[@tb2748]

@@MathematicsTutorAwesome, thanks!

[@lazyonigiri5665]

why did you choose 0 & 2?

[@user-vq2xq9tp8g]

Thank you so much🤍that was really useful!

[@iamacat9742]

This guy sounds like Indian Morgan Freeman

[@josepht11]

Why cant it have 3 roots with it being a cubic function?

[@MathematicsTutor]

A cubic equation will always have 3 roots. Combination can be 3 real roots all of order 1 1 real root (order 2) + 1 real root (order 1) 1 real of order 3 1 real root + 2 imaginary roots

[@josepht11]

Thanks alot for the quick reply, i get that but you proved it doesnt have 2 real roots, do you not need to prove it doesnt have 3 real roots?

[@MathematicsTutor]

We wanted to prove that it has only one root. If it has more than one root then there should be a turning point. The explanation that it cannot have two roots also cover the three roots conditions. Hope that is clear.

[@josepht11]

Anil Kumar yes very clear thanks alot!

[@jaisinghsaharan7846]

Anil Kumar sir upload advance questions on mean value theorem

[@dwightlim4820]

Hello! How do we prove that a function (x^4 -4x +1) has exactly 2 real roots using rolles' theorem? Since f'(x) can be 0 for this case?

[@labrospnevmatikos2402]

Dwight Lim you use three roots in rolle’s theorem

[@Am_Qaid]

اللي جاي من محسن الشهراني لايك 😂😂😂

[@ipekosmanoglu7770]

Aaaa sınavım var sınavımm

[@rahulsakharkar4927]

This proved that the function does not have two real roots, but that does not mean it has 1 real root, it can be 0 also. Your didnt prove that part, it has exactly 1 real root

[@thabomaleke874]

If a function cannot have two roots, then it definitely cannot have 3 or more real roots 😢

[@樊伯遠Auston]

GORLOCK THE DESTROYER THE BEST GORGORGOR

[@varshithkumar2251]

i am sorry

[@lifeislikeatoiletpaper.6762]

????

[@frovat]

thank you so much!