❖ Finding Local Maximums/Minimums - Second Derivative Test ❖

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Finding Local Maximums/Minimums - Second Derivative Test. In this video, I discuss how to use the second derivative test to find local maximums and local minimums. The basic idea and a few examples are shown!

[@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

[@groggsmcgee3293]

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

[@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!

[@patrickjmt]

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[@patrickjmt]

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[@patrickjmt]

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

[@Prophetelf]

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[@patrickjmt]

@letthemxeatcake no problem, hope it helps.

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[@kevinr515]

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[@patrickjmt]

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

[@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.

[@annamaylabrador3759]

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

[@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

[@tadashi7249]

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

[@patrickjmt]

you are welcome! :)

[@stefaniea7312]

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[@tousef01]

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[@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.

[@vanillabri4198]

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]

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[@patrickjmt]

@DJSt3v3n no problem!

[@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.

[@KoreaXFan]

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

[@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.

[@normaazgomez9330]

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

[@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.

[@enockmwanza9643]

this has really helped me

[@alasgar_alakbarov]

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

[@NJA2k8]

my calc test grade will thank you tomorrow

[@porkypine602]

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

[@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!

[@ashwithchandra2622]

you are the only who saved me in calculus

[@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

[@nouraelsaadany4860]

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

[@cmone3955]

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

[@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!!

[@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

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[@hondacivicgang3800]

THE LEGEND

[@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.

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

[@jessicakim2129]

How did you get 4x(4-x^2) for the second derivative?

[@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.

[@the81kid]

Once again, many thanks!

[@patrickjmt]

@rpsc06 no phd

[@Constantinople5]

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

[@bafedilemokonyane8924]

thank you sooo much this helped me so much..

[@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. :)

[@letthemxeatcake]

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[@qq-px5jj]

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[@patrickjmt]

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[@RealEverythingComputers]

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[@patrickjmt]

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

[@qanhdang4035]

nice work, very easy to follow.

[@patrickjmt]

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

[@leonardmwandikwa3973]

nice one man, thanks for the clarification. awesome

[@jojogirl2008]

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

[@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.

[@lilpwincess9406]

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

[@polarisgal]

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

[@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.

[@Anonymous2094]

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[@Corrup7edChaos]

thanks for the help!

[@kelvinwells9541]

Thanks dude....coming in clutch.

[@patrickjmt]

@sxswitch glad i could help : )

[@hakarhussein599]

Thanks alot 🌹🌹🌹 It is useful

[@Mehrnaz926]

I totally agree, you do have nice hands.

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You are a life saver

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[@ryukomatoi7113]

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[@Kwr94]

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[@dragonevil32]

thank you so much

[@flareb99]

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

[@SKOOKaVISION]

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

[@davidturay4160]

Fantastic very helpful

[@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.

[@mthfku]

Thank you

[@patrickjmt]

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

[@isabellaagosto2990]

thank you!

[@XCrystalXClearXLoveX]

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

[@Orionzeus05]

Simple now, thank you :)

[@poonyisatongkhamsai9027]

thank you sooooooo much

[@Seunia]

How do I know whether to use the first or the second derivative to find the local minimum and maximum? In your other video, you used the first derivative. Thank you for all those maths videos by the way. They are very helpful :)

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[@user-jd8of1tw6l]

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[@ennie0728]

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[@rpsc06]

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[@lina_cats]

don't we have to check the first derivative for increasing/decreasing.Its local max/min only when it changes sign of a function from plus to minus and vice versa,when the second derivative value is positive,it means its concaved up but not necessarily a max/min?I had examples where those were inflection points just.Correct me if i am wrong please,thanks

[@mikescannell4575]

Do you plug your critical number solution of the second derivative into the original equation?

[@camillolin73]

Without you, I don’t know what I would have done...

[@iviriya]

thank you

[@Ishq786]

There is a (-) in front of the x^2 is separate, so whatever value the x^2 gives, it will become (-), so it is actually like this -(x^2). For example: -(2^2) = -(4) = -4.