❖ Finding Local Maximums/Minimums - Second Derivative Test ❖

[@mustafamalik4211]

Here are the steps: 1) Find the 1st Derivative 2) Find the Critical numbers by setting the numerator of the f' = 0 3) To see if its undefined, plug denominator = 0 4) Go back and take f" 5) Plug in the Critical number in for f' & f", you see if you get a positive number out 6) If f" Positive Number = local minimum. f" is negative = local maximum 7) Done!

[@al-maalaalmaawali260]

forget little thing.. if its 0

[@pierreboutin448]

@@al-maalaalmaawali260 if you put the c value in f"(x) and its 0 that means you found the turning point of the curve

[@patrickjmt]

yes, i agree! i strive to point out minor mistakes using annotations, and simply delete vids that have more serious mistakes. the last thing i want to do is teach someone incorrectly or make a huge, confusing mistake!

[@groggsmcgee3293]

You are the reason I am surviving calculus. Thank you for this.

[@asadbilal591]

By far the best math teach iv found so far on youtube. Better than Khan Academy.

[@patrickjmt]

+Asad Bilal thanks! Come back any time!

[@jgc9199]

Khan academy is vague in calculus it's not that good. I prefer this channel or the organic chemistry tutor.

[@nellycorture]

I honestly dont understand why i even go to class anymore. It is such a waste of my time! I go for 2 hours a day to calculus learning absolutely NOTHING, then i come home and watch this 11 min video it all makes sense! Thanks for the vids, you saved my life countless times :)

[@KoreaXFan]

YES. you have this videooo!! I slacked off after derivatives and was falling behind in class. This will catch me up :D

[@kelvincheng999]

Brushing up for my calculus 1 final in 3 days. You are the reason why I'm passing this course

[@patrickjmt]

@L4ctose thanks for your useful comment. it is valued and appreciated!

[@catharticgemini]

In the first minute alone you helped me more than my professor

[@Trexxx04]

I know you've gotten this comment thousands of times but this literally just cleared up hours of lectures and frustration, brilliant channel thanks so much

[@kevinr515]

thanks so much, none of my math professors and TAs can speak clear english and this is saving my life. Kinda getting mad at youtube for ads in the middle of the video. But keep up the great work

[@tadashi7249]

You don't even know how much this helped me!! Thank You!

[@patrickjmt]

you are welcome! :)

[@judieakkad4507]

best math tutor on KZbin so far, Thanks a bunch! :)

[@sxswitch]

This helps a lot. I already knew how to do everything but when my teacher introduced the more than or less than zero for the second derivative, he confused me completely. This video cleared everything up.

[@AFCoulthard]

I would say that most of your videos are perfect length. You usually describe to me perfectly what would take an entire lecture or two lol.

[@alasgar_alakbarov]

you are explaining better than my teacher. Thank you for this.

[@patrickjmt]

look just below the ratings (all the red stars) and to the right. it is just below the 'run time' clock

[@per-5786]

Patrick for president. Thanks heaps!

[@patrickjmt]

@kevinr515 glad to help! thanks for letting me know about the ad in the middle - it should be gone now!

[@RealDarkFilm]

I like you calculating at this speed because if you go too fast, it is hard to keep up, whereas if you go at a steady speed, it is easier to comprehend. So keep up the good work bud! You aren't doing anything wrong

[@darrinjamminn360]

patrickJMT, I am passing Calculus because of you. You are awsome. Thank you so much!

[@despindola10]

thanks to your channel i can officially not be worried when i go to class for a quiz or a test :) thanks for this!!

[@cieran555]

did this in leaving cert and forgot! now i am doing it in college! remembered in after the first min of the video! THNK YOU. you have helped to pass maths in College!

[@DawnOfHenry]

you are a god, this example was the exact question i was trying to work out! love the videos, like a second teacher to me

[@annamaylabrador3759]

I definitely love your way of teaching it!! thanks a lot !!

[@Constantinople5]

Your videos are a life saver! I would probably be failing calculus without these videos.

[@NJA2k8]

my calc test grade will thank you tomorrow

[@porkypine602]

thats crazy 5 years ago u were and calc and now im in calc

[@patrickjmt]

that is what a friend who i was perpetually in love with growing up used to always tell me : )

[@RhymelessWater]

These videos saved my life. From a D in AP Calc BC to a B in 3 weeks. :D And now I'll be getting an A this quarter.

[@ashwithchandra2622]

you are the only who saved me in calculus

[@dr.nigamanandamishra1946]

I got three weeks to study for a calculus test. I didn't. Then I solved some question yesterday(It's 6 am here now) and realised I am way to shitty at it. Then came in your videos. Thanks a lot dude, Test scheduled at 10am.

[@patrickjmt]

@DJSt3v3n no problem!

[@qwerty74]

Thank you Patrick! :D My final is on this Wednesday and this particular video just unlocked the last closed door in my brain regarding the extrema.

[@Prophetelf]

These are crazy helpful dude, thanks a lot!

[@patrickjmt]

i still do not mind hearing it ;) glad i could help you

[@maicolll]

If I actually manage to get my degree after some years.... I will donate to you since u have helped me so damn much

[@patrickjmt]

@letthemxeatcake no problem, hope it helps.

[@sarinatak]

Thank you..... I have a test for tmrw, i was stuck in this problem Your.vids. has reallyyy helped in these derivatives,concavity, increasing ,.... Im really good at math,but i dont understand anything since we started calculus Thanks alot. :)

[@SKOOKaVISION]

This is great, much simpler than having to do numerical analysis with the first derivative every time.

[@XCrystalXClearXLoveX]

hahaha, lovely singing voice! i love your videos!! Im desperately trying to prepare for my math finals in 2 days! wish me luck :)

[@cmone3955]

Watched the first 1 min... gets the second derivative test ... ohhh thank you CALC GOD !

[@nouraelsaadany4860]

Because of your videos I have passed math 3 .. thank you so much

[@polarisgal]

great video, lost my notes and this really help. thanks.

[@patrickjmt]

@richindiankid that sounds like a good idea. with a name like ' richindiankid ' i hope you gave a LOT! : )

[@paris0818]

You are an excellent resource. I hope by reviewing your videos, I will be able to pull up my grade in calculus. It's been 30 years since precalc.

[@normaazgomez9330]

Oh my, how did I forget this! Thank you again!

[@zainshahid1792]

You are the hero we dont deserve

[@KoolGNasBlackThought]

do you have any vids with really messed up examples? Like with e, ln, exponents and all that?

[@khoinguyen22]

You still use the same logic just applying your knowledge of derivative of natural logs e's and etc. If you need help with doing derivative of those you should just brush up on that.

[@flareb99]

this should be on trending every week #G.O.A.T.

[@patrickjmt]

it would still work. since the second derivative is always positive, it would mean you have found a local minimum

[@patrickjmt]

@sxswitch glad i could help : )

[@vanillabri]

omg thank you so much for this video I'm doing calc homework right now and it is this exact same problem!

[@danielbaez1991]

same here 😢

[@gennkill]

+bri farris same he.. not... LUCKY KIDS

[@hondacivicgang3800]

THE LEGEND

[@tousef01]

These videos have helped me so much, thank you!

[@letthemxeatcake]

THANK YOU THANK YOU THANK YOU! I need to study this for my exams!

[@Kwr94]

GOD you are such a lifesaver! Thank you so much

[@enockmwanza9643]

this has really helped me

[@kelvinwells9541]

Thanks dude....coming in clutch.

[@stefaniea7312]

Thank you so much! This really really helped me! I have a test tomorrow and I was so clueless. Thanks so much! :)

[@Eadaoin94]

@patrickJMT I have to say I agree... but only because I have a massive test in algebra, differenciation, matrices and integration tomorrow and I'd love some fast cramming videos... but good videos!

[@thealbinohobo33]

great video. heres a suggestion though, if you could put the steps in the description it would help a lot (i.e. step 1 find derivative, 2, critical numbers, 3 plug critical numbers in)..but great video!

[@deveshangovender3825]

Dude you're a life saver thank you so much

[@the81kid]

Once again, many thanks!

[@rdjm555]

The critical points of the second derivative are the possible point of inflection. The critical points of the first derivative are the possible local/absolute max or min. If the critical points (except VA) in the first derivative is substituted to second derivative and is greater 0 there is a local min at that point on the graph and vice versa.

[@Mig440]

Very good explanation of a, sometimes, difficult method to understand ;)

[@PengunaFilms]

YOU SAVED MY LIFE.

[@qanhdang4035]

nice work, very easy to follow.

[@rpsc06]

Why aren't you a university prof, your better than all my math profs combined!

[@Constantinople5]

@rr5001 Generally, calculus is split up into 3 classes, Calculus I, II, and III. Upper division courses might include differential equation and muli-variable calculus.

[@Anonymous2094]

Thanks a lot for you useful video, Sir. It's been grat help. :)

[@leonardmwandikwa3973]

nice one man, thanks for the clarification. awesome

[@itachiuchiha6940]

You are a life saver

[@citizenofvirginity]

@SamBM17 That's the derivative of the bottom of the second derivative (x^2+4)^"2" = "2"('x^2'+4)('2x'). The chain rule.

[@qwerty74]

hahahaaaaaa you are halarious xD! Thank you veeerrryyyy much!!! I'm gonna be honest with you and say that I have a somewhat powerful sixth sense... I come across things/events before they happen... The only thing I can't come across is questions in an exam, not even a quiz!... I swear this is so frustrating!... I sure could use wireless info transfer directly to my brain! wooot woot! :D

[@manassaini3912]

Wait I have a question. Thank you so much I understood everything, but what is the point of finding the second derivative to find the local max's and min's when you can just take the critical points you found, -2 & 2, and making a sign chart as you did in the previous video. That's what I did and still got the same answer.

[@AddicProductionsEE]

Have a Calculas exam in an hour, after this I'm gonna make this test my bitch. Thanks a million!!! :)

[@geraldortiz7281]

at 2:20 where 2x goes?

[@AliHasanAli]

+Jayz Ortiz -x(2x)= -2x^2, he added that to x^2+4, and the result became -x^2-4 as it is shown at 2:20

[@qq-px5jj]

thank you for this video sir ❤️

[@sumantapanigrahi3765]

You deserve 10M

[@patrickjmt]

@rpsc06 no phd

[@bafedilemokonyane8924]

thank you sooo much this helped me so much..

[@jojogirl2008]

thanks so much! it was great like always! :)

[@RealEverythingComputers]

Thanks great video!

[@RenzGonzagaTV]

im smiling so much because you helped me understand this so well...am i weird? lol

[@hakarhussein599]

Thanks alot 🌹🌹🌹 It is useful

[@guitarsea003]

do you have videos wherein you apply maxima and minima to word problems? :)

[@qasimkhan-oc8hk]

where did the +2 come from at 6:05

[@Mehrnaz926]

I totally agree, you do have nice hands.

[@SamBM17]

Hi Patrick. Where you've differentiated f'(x) so f''(x) = (x^2+4)(-2x) - (4-x^2)2 x (x^2+4)2x where does the 2 outside (4-x^2) come from? I hope my question makes sense, thanks

[@davidturay4160]

Fantastic very helpful

[@lilpwincess9406]

great help...thank u so much...

[@mariahlowery6848]

More applications of derivatives please!

[@patrickjmt]

@LucLamontCaputo well, a math phd is not easy. and i do not want it. i dont want a uni prof job

[@cristobalgarces1675]

Strayed too far from Calc 3 and now I'm watching Calc 1 videos now. Wish I could go back to the easier stuff.

[@Wyzmayne01]

good stuff.

[@meawmapiti3607]

Thank you so much for the video ^_^

[@Sasha7amad]

The way you say "excuse me" is just so cutee! I hope you got over the fact that you've got some creepyy students lol

[@patrickjmt]

@guitarsea003 optimization problems

[@Corrup7edChaos]

thanks for the help!

[@triplenick]

What happens if you are given a closed interval? For example, [-3,5]. If f''(-3) = negative and f''(5) = positive, is x = -3 a local max and x = 5 a local min? In my class, the interval can be included in the local/absolute min/max.