FIRST DERIVATIVE TEST to find the max and min (KristaKingMath)

► My Applications of Derivatives course: www.kristaking...
The first derivative test is the tool you use to test the potential critical points of a function to see whether or not they are actually critical points. You can use the first derivative test to describe the behavior of the function on either side of the critical point. Or, to put it another way, you can use the first derivative test to say whether the function is increasing or decreasing on either side of the critical point.
If you can use the first derivative test to show that the function is increasing on one side of the critical point and decreasing on the other, then by the first derivative test you've proven that the potential critical point is an actual critical point, and therefore that the function has at least a local maximum or local minimum there, if not a global maximum or global minimum.
In order to use the first derivative test, pick values on either side of the critical point, and plug them into the first derivative of the function. If the result is positive, then the function is increasing on that side of the critical point. On the other hand, if the result is negative, then the function is decreasing on that side of the critical point.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@aaronpicking4935]

Krista, when I graduate with a degree in Engineering Physics in a few years, it's going to be incredible to know how many people you helped with these videos. I got 100% on my last calc I test. Thank you!!

[@kristakingmath]

Congrats on your test! It makes me smile that I can help along the way. :)

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[@kristakingmath]

I'm glad it could help!

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This video can help me🤓, Btw im first year college, "SALAMAT" is Thank you☺️

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I UNDERSTOOD EVERYTHING SHE SAID RIGHT FROM THE BEGINNING OF THIS VIDEO/ THANK YOU SO MUCH ! :)

[@kristakingmath]

You're so welcome! I'm glad it could help. :)

[@fireemblem2770]

I'm not sure what I am paying for my calculus class this year, but I will pay you that amount, because I am actually learning from you. This channel is simply fantastic.

[@kristakingmath]

Thank you, Fire, I'm so happy to help! :)

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These videos even manage to put Kahn academy to shame. One day all maths lessons will be taught through use of them. It will take time, but your work will become eternal.

[@kristakingmath]

Jack White Thank you so much!

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Why u pulled khan here? And moreover ,why are u comparing Krista with Khan or vice versa? Anyway, she teaches good.

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Jack White
Khan Academy is shit

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You are very good!!!!

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You're a life saver Krista! I spent so much time re-reading my lecture notes multiple times trying to understanding with no avail, but watching your videos and hearing your explanation makes it so much clearer. Thank you very much!

[@kristakingmath]

You're welcome, I'm so glad it helped!! :D

[@anannoyedpanda]

Prepping for calculus finals in college. This video was a lifesaver for a review. Thank you.

[@Successer]

crazy how this is now Hi-school material

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Thanks a lot, you've helped me understand more in this video than I did a whole week of lecture.

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Your work is so clean and thorough, thank you!

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I am TERRIFIED by math. Right now I am taking a calculus class, and your videos are SO much better than the learning platform my school uses. Your videos make math a bit less scarier, and are right in line with the class' curriculum. Thank You!

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I understand everything but of your explanation with free of charge. Thank you so much.❤

[@kristakingmath]

You're welcome, Kara! I'm happy to help! :)

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OMG i understood everything she said and she has a talent that she brought my attention the whole 15 min i was so fouced THANK YOU

[@joshmorel2363]

Thank you for being so calm and helpful

[@fireflies15]

I cant believe how easy and clarifying this video was. Just wow. You practically saved me from eternal confusion thank you so much

[@josemendesdemoura2581]

Hi I'm brazilian and i follow your channel and this help me a lot in college , Thank you so much !!

[@kristakingmath]

+Jose Mendes De Moura So glad I could help!

[@ahsantanveer7366]

THANK YOU .. Maths have never been this much easier :)

[@yeny7194]

wow, so thorough, clear, and precise. Goes very well with the explanations on the textbook. Thank you !!!!

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Thanks..!!!! That's really helpful for my Exam Study...!! :D

[@kristakingmath]

Awesome! Thanks for letting me know.

[@prrtygrrl1]

Thank you so much!! This connected so many dots for me and now it is making sense!

[@katherinel8970]

I love your handwriting! makes understanding so much clearer :)

[@kristakingmath]

Thanks, Katherine! :D

[@ddharsh2548]

You've made my journey as a mathematician smoother, and I'm incredibly grateful for that! So, thank you, thank you, thank you so much!! I feel like I finally understand something really well to the point where I can teach this to someone else. :)
Also, even if your videos are old, they are still high quality, wow!

[@kristakingmath]

Thank you so much, DDharsh! I'm so glad the videos have been helpful and that you've been getting good use out of them! :)

[@hollymenna3659]

I watched three different tutor's (paying for one, he is good, but his vids on this were not as good and I understood after watching this video ONE TIME!) THANK YOU!

[@kristakingmath]

Aw thanks, Holly! I'm so glad it could help! :)

[@md.wasiffaisal5463]

Clear and Concise, loved it :)

[@merhabamuhemmed3990]

I fad up from math classes , even after 4 days our midterm exam will be , while hearing your explanation I start to confidence myself , thank you so much for you ! from Uyghur

[@kristakingmath]

You're so welcome, I'm so glad the videos are helping to clear things up! :D

[@shahriarfahim9257]

you are awesome... its how you explain things which make every math easy and finally helps me to get good marks :)

[@kristakingmath]

I'm so glad it's helpful!

[@Rivin2e]

wow, i was able to understand this better in your sub 20 minute video than i was in my hour and 30 minute class. Thank you for this video!

[@kristakingmath]

You're welcome, I'm so glad it helped! :)

[@Picklejar75]

best explanation on youtube, this was so clear to me.

[@kristakingmath]

+Picklejar75 Thanks, I'm so glad it helped!

[@kevind3946]

The best video I've seen explaining this topic. Thank you!

[@kristakingmath]

😊

[@coloredpandas1993]

When I'm in calc class while my teacher is teaching I'm watching this and writing notes from this video instead of his lecture. Guess I'm just there for the attendance grade XD

[@hajiaslam3963]

Lol

[@architjain9754]

This was a very nice video ma'am. U explained it quite well.Sincere thanks from me

[@jazzalfarij1984]

Probably the first time I enjoyed doing math.

[@bek5810]

video is very helpful and clear. you took time to explain every detail. very helpful, thank you

[@kristakingmath]

Awesome! Glad it could help. :)

[@jorialdridge7182]

SAVED MY LIFE! thank you so much for breaking everything down

[@kristakingmath]

I'm so glad it could help! :)

[@bheeshmayo8354]

[If in question if they didn't mention any range of function then assume it to be
(-∞,+∞) excluding points where function is not defined ]
I guess if a function rangers from (-∞ ,+∞)
As it is open interval i.e, not extream points
then, we can't find global Maxima or global minima . In other words we can only say local Maxima and local minima
And we can only find all the global & local {max, min} iff the given interval of the function is close i.e, [a,b]

[@ProfessorAmandaSartor]

For the book I use, -1, 0, 1 are critical points even before you check withe number line. They define critical points as the values where the derivative is zero or undefined. Then you use the first derivative test to determine if those critical points are relative extrema.

[@kristakingmath]

True! I've seen it done one of two ways: 1) The way your textbook does it, where all values at which the derivative is 0 or undefined are "critical points," and then you use the first derivative test to classify those critical points, or 2) Values at which the derivative is 0 or undefined are "critical numbers" or "potential critical numbers," and then you use the first derivative test to verify where the function actually changes direction, and those "potential critical numbers" that lead to a change in direction are then the "critical points." :)

[@kkamous7278]

I am very thanks to you for this video. your vidio give me a lot of help. you're great. I love your work . you're are the best teacher in the field of mathematics. you work for people . may you live long.

[@saisripavi]

Krista, I'm saisri. Loved your video. Super pakka Explanations and you have literally saved my exam. Thankyou so much. In India its 7.30 pm now and it's so perfect for me to prepare for the next hour. Thanks.

[@kristakingmath]

Hi Saisri. I hope it went well! I'm glad it could help. :)

[@luiszapatac]

old but gold

[@mohaimahmacod6123]

I been struggling in my calculus subject until I watch this video.

[@kristakingmath]

I'm so glad it helped, mohaimah! :)

[@sivaprasad9601]

Thanks a ton for the video.
Could you please explain how to find the global max and min without plotting the curve for any equation.

[@clevsy]

Thank you so much, that was very clear! Really appreciate the quality!

[@kristakingmath]

+Clever212 Thanks for letting me know!

[@earlmijares1657]

Thanks a lot, Krista! After I watched your vid, I think I can almost pass my quiz. Cheers from PH!

[@kristakingmath]

I hope so, good luck on your quiz! :)

[@binite3826]

You make it so much easier!

[@Teyros]

Beautifully taught!!! everything i needed to know thank you so much

[@kristakingmath]

Thank you, Taylor, I'm so glad it helped!

[@manojmano5239]

Perfect 🥰 explanation thanks from india

[@kristakingmath]

My pleasure, Manoj, I'm glad you liked it! :)

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You're a blessing. Thank you so much. I've never understood a topic so well :')

[@kristakingmath]

You're welcome! I'm glad it could help!

[@abdullahbukhari1469]

Thanks alot sista you really explained it beautifully well, I hope TH-cam is paying you heavily. In my country we use the terminology Absolute and Relative Extrema.

[@margaretmoreno1311]

Thank you for sharing this video. I can finally understand it now.

[@kristakingmath]

Awesome! I'm glad it could help!

[@harisosman64]

Very useful video! Thank you!

[@kristakingmath]

You're welcome, haris! I'm so glad it helped! :)

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Thank you so much!!! everything that i was looking for!!

[@kristakingmath]

+Seamus Deakin You're welcome, I'm so glad it helped!

[@Zveir]

Thank you so much, this was more clearly explained than anything else. I might actually do well on my upcoming exam >.>

[@craftingodst3400]

You helped me alot! Thank you so much

[@kristakingmath]

You're welcome, I'm so glad I was able to help! :D

[@renan6827]

That is a great video. Thank you so much

[@kristakingmath]

You're welcome, Renan! I'm so glad you liked it! :)

[@andreaprado112]

Thank you soooo much ❤

[@tb2748]

what if your function, f(x), is undefined at certain points? would you include those points where f(x) is undefined in your number line?

[@nardinomuchongo6080]

Thanks Ma'am

[@ruhulquddus6890]

Many many thanks

[@zahraaahmad1334]

I had difficult time because of my quize calculus tomorrow but after a watch this video i feel confortable finally i andrstaand this thank you very much 😿😩

[@sentattiayyanartemplevarth3561]

thats really good....and it is very useful to me...thank u

[@emiljacksonlyngdoh5479]

Very good explanation.

[@kristakingmath]

Glad you liked it! :)

[@kelvinmakuyana1050]

that was so clear .........thanx alot

[@kristakingmath]

Awesome! Thanks for letting me know.

[@TokiBird]

you're honestly perfect. thank you so much! i have a test on this tomorrow >_

[@kristakingmath]

+Nangtucket Island Good luck! Hope you rock it.

[@abhishekkhandare8045]

what a video daam ausam .... please can I do a video on lefthand and right hand derevative

[@vusalmammadov334]

Thank you, Krista, for the clear explanation :) I just wanted to ask can we draw a conclusion that (0,0) is a local max without looking at the graph ? Because it is not always easy to sketch the graph.

[@kristakingmath]

Yes, you don't need to sketch the graph at all. You can draw the conclusion just from the little line graph that we made, where we put the critical points -1,0,1 on the number line and looked at the behavior of the graph in between those points. The only reason I showed you the graph was to prove to you that our work was correct, but you never need the graph to draw a conclusion about the local extrema.

[@vusalmammadov334]

Thank you Krista :) That was really very helpful :)

[@jeffkamuthu3276]

very helpful be blessed

[@SatishNatarajan]

Thank you for the wonderful explanation

[@kristakingmath]

Glad it could help!

[@petargameplay2998]

Very helpful video thank you!)
I have a question.. at the first derivitive test couldn't i just use the interval`s method so if the higher power coefficient is a positive then we start with + at the right side and we swap it to + - + - + -.. from right to left
like in this case 4x(x+1)(x-1), we see that highest power coefficient of x is + so we start + , - , + , from right to left -. Just like u did.

[@MAEVAROBERT-ro5wl]

Thanks so much 👍😊

[@kristakingmath]

You're welcome, Maeva! :)

[@-OnionTerror-]

Dear Ms King! I have a very similar problem that I have to work through, the only difference is that my derivative is 4x^3 - 4x + 1. its this +1 on the end that is really confusing me. how would one deal with it?

[@thesunfirecape]

what do you do if you cant factor what you get in the
first derivative test?

[@mohamedshnaiba9003]

That was very helpful thank u

[@kristakingmath]

You're welcome, mohamed! I'm glad it was helpful! :)

[@buddhikajayasekera1407]

Life Saviour!

[@flyeraerospace8353]

Very good explanation... thank you so much for this awesome video :-)

[@kristakingmath]

+Behnaz Neuforge You're welcome, I'm glad you liked it! :)

[@sagargurung8682]

thanks alot... it helped me too... i have an exam today...

[@kristakingmath]

+Sagar Gurung I'm so glad it helped, good luck on your exam!

[@systemforge]

Thank you :)

[@tannerthornton7850]

Very helpful! Thank you so much! I hope I can credit you with an A tomorrow 😬

[@kristakingmath]

You would definitely still deserve the credit... I hope it goes well!

[@cinakakar197]

Love it
Thank you

[@NyeinNyeinEI-y8k]

Thanks

[@kristakingmath]

You're welcome! :)

[@hephaestus1956]

thank you so much, u dont know how much this means to me

[@kristakingmath]

You're welcome, I'm glad it helped!

[@zainislam554]

what to do if we have only one critical value? how to plot it on number line?

[@kristakingmath]

You still just plot the one point on the number line, then pick test values on either side of it. If your single critical point is x=5, use test values of x=4 and x=6, for example.

[@albertoaldana-cabello6804]

it seems that most videos just use the most simple examples, I hope they would do more complex exercises.

[@zakwantermizi6642]

tq for the informartion :)

[@user-vf9lv2yc6q]

Thanks a lot you saved me but My teacher used a table to test the derivative not a line could you please do video using table😁..

[@daydreamer2315]

Love your voice

[@huntforerror]

THANK YOU

[@slimrunner_4928]

You and my professor used easy examples to solve 😣 but I understand a little bit better.

[@mikey-nm3od]

great videos

[@Munchkie]

u forgot to also states its also a local min/ global min is also the local min

[@enzowoods288]

Hi Kristina...!!!

[@mozkau_gaming]

Thank you, i figured my mistake.

[@kristakingmath]

So glad it helped! :D

[@yemiabadariki9572]

How do we find the derivative of min(x,y)

[@mk9834]

I love your lovely voice♥ so much

[@aznsuperman9]

id rather have you as my math teacher than my current professor =.=

[@Ryan-pu5fs]

Great vid

[@kristakingmath]

Thanks, Ryan!

[@karimjiwa9279]

You're a God!! Thanks.

[@MuhammadNawaz-rc6wk]

Thnk u madam ♥

[@kristakingmath]

You're welcome, Muhammad! :)

[@luiszapatac]

omg this is cool

[@saiphislam9396]

I wish she was my maths teacher o I wouldnt ever fail, PS somebody plx drop any method of contacting her? have some questions :(

[@waledGamer]

thnx

[@kristakingmath]

You're welcome! I'm glad it could help.

[@MrGatz007]

Great video! Tyvm!!!!!!!!