Finding Stationary Points and Determining their Nature

www.mymathsguy.com
Learn what the Stationary Points of a function are, how to find them, and how to determine their nature using either a nature table or second derivative test.
0:00 What are stationary points?
1:30 Gradient and derivative
2:45 Finding the Stationary Points
6:20 The three types of Stationary Points
7:00 Determining the nature of the Stationary Points
10:30 The 2nd derivative test
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Gary

[@gucciashton4731]

Fabulous to find a Scottish maths tutor on KZbin. I'm from Edinburgh and doing a Maths & Stats degree now, this video was super helpful.

[@mymathsguy2707]

Nice one, thanks for letting me know it was helpful, much appreciated!

[@magdakwiatkowska7929]

I had a major problem with this and did not understand it at all at school. Thank you so much, you, really helped me and explained everything so clearly ❤

[@mymathsguy2707]

You're welcome Magda :) I'm glad the video was useful to you and it's really nice of you to let me know!

[@deliveringIdeas]

What an absolutely beautiful and eloquent explanation of an otherwise complicated topic. Thank you for this sober and transparent elaboration.

[@mymathsguy2707]

No problem, I'm glad it was helpful to you :)

[@augustusprime0_o]

This was so helpful. Thanks!

[@user-xx9zo5ul6l]

You're the best sir

[@B4Bwarrior]

You have no idea how much this helped me thank you 🙏

[@mymathsguy2707]

I'm really happy it helped, thanks for letting me know! This motivates me to make more videos. I just recorded a new video on a similar topic which may also be useful to you kzbin.info/www/bejne/l4OXeGSEoLqriLc

[@tailsgfx]

helped loads, thank you

[@mymathsguy2707]

You’re welcome 🙂 Thanks for watching!

[@PROofHAPPYWHEELS]

Thank you

[@mymathsguy2707]

No problem :)

[@richards_greatman]

This was very helpful. Bless you tutor.

[@mymathsguy2707]

You are very welcome friend! I’m glad it helped you out :)

[@gregorkemp1131]

This helped me a lot when trying to pass my tests thank you for explaining it so clearly:)

[@mymathsguy2707]

You're welcome. I'm really pleased to know that my video helped you out - thanks for watching :)

[@vaibhav2831]

Thank you very much

[@mymathsguy2707]

You're very welcome, thanks for commenting :)

[@dhyan3421]

that nature table trick is sooo clever!!!!!!!!!!!!!!!!!!!! im blown away by how simple you just made this!!!😂😅🤯

[@dhyan3421]

ps: i will sub to u.... for sure

[@mymathsguy2707]

I'm glad it was helpful to you. It's essentially a mini sketch of the graph and, with some practice, should be a straight-forward process. You can also use the second derivative of the function to determine the nature of the stationary points - but I like the table because it basically shows you what the graph looks like :)

[@dhyan3421]

@@mymathsguy2707 yea same :)

[@aminahrazzaq1674]

This sis o helpful. Thank you. the explanation was flawless.

[@mymathsguy2707]

:) That's great to hear, thanks for letting me know

[@Predemelsolutions]

Great explanation there. Thanks

[@mymathsguy2707]

You're welcome Christian, I'm glad the video was helpful :) I appreciate you taking time to comment!

[@amyroberts-nurse7369]

Thanks for making things look simpler

[@mymathsguy2707]

Thanks for watching my video - I'm happy to know that it helped you out :) And thanks for commenting - I really appreciate that!

[@stevenmwangalasuzzy3590]

Please keep doing this 🙏🙏🙏🙏God bless,you really helped me.

[@mymathsguy2707]

Steven, I'm very happy to know the video was helpful, thanks for taking the time to comment :)

[@kaibluck1380]

your explanations are amazing🤩

[@mymathsguy2707]

That's great feedback to receive, thank you for taking the time to let me know :) Here's the link to a new video I just recorded on curve sketching which uses similar techniques. It may also be useful to you kzbin.info/www/bejne/l4OXeGSEoLqriLc

[@user-dc8hl4jh2d]

Very detailed explanation! Thank you Sir!🥰

[@mymathsguy2707]

Awesome, glad it was helpful to you! :)

[@tasfiadiya6042]

this video is really helpful. Helped me a lot in exams , thanks !!

[@mymathsguy2707]

Awesome, I'm happy to hear this! Thanks for the comment :)

[@nanaamaankomah70]

Thank you Sir 🙏🙏you’ve really helped me out🥳🥳🥳I now love this topic 🥰

[@mymathsguy2707]

You're welcome . . . feeling the love for stationary points, awesome! 😅

[@mubitanosiku2904]

Thank you sir

[@mymathsguy2707]

You’re welcome :) Happy that the video helped you out

[@Vyola08]

Excellent

[@mymathsguy2707]

Thanks for commenting :) I'm happy to know the video helped you out!

[@xdgaming952]

You really are my maths guy :) thanks for this!! I always keep forgetting what to do after finding the derivative!

[@mymathsguy2707]

HaHa thanks! I know right - you differentiate and then different questions require you to do different things with that derivative, not easy! Just gotta keep on practising :)

[@xdgaming952]

@@mymathsguy2707 Sure, Sir! Thank you too and you're welcome!

[@yomba675]

Thankyou Sir. Clearly understood💯🙏

[@mymathsguy2707]

You're welcome friend 🙂I'm glad it was useful to you - thanks for commenting!

[@ayman4884]

very helpful thankyou

[@mymathsguy2707]

Thanks for watching the video and for taking the time to comment, much appreciated. And happy to know that it was helpful!

[@jenesiahhutchinson4785]

This was very helpful, thanks❗😭❤

[@mymathsguy2707]

You're welcome, I'm glad it was useful to you.

[@johnbestsebastian2267]

This was really really helpful Thank you Sir..

[@mymathsguy2707]

I'm happy to know that it helped and thank you for leaving the comment, much appreciated!

[@henryhunter1773]

A really helpful video! Thanks for the upload!

[@mymathsguy2707]

You're welcome, I'm glad it helped you out. I'm going to upload a new video with an alternative technique soon - I'll send you the link when I do in case it's of interest :) Thanks

[@henryhunter1773]

@@mymathsguy2707 I'm looking forward to it.

[@mymathsguy2707]

@@henryhunter1773 kzbin.info/www/bejne/rnaml31nac-ko80

[@official_jemma]

BROOO you saved my life tysm!!!!!!!!

[@official_jemma]

same!!! omgosh

[@official_jemma]

sheeeeeeeeeeeeeesh

[@mymathsguy2707]

You're welcome buddy. Glad it helped you out. Just proves the point that Math Saves Lives 🙃

[@gee429]

Good explanation

[@mymathsguy2707]

Thank you. I'm glad it was useful to you.

[@pyronsue7592]

thank u very much

[@mymathsguy2707]

You're welcome, thanks for the comment. I hope the video was helpful to you.

[@hennesseyufc6300]

thank you so much have a maths exam in 1 hour this helps a lot thanks sir

[@mymathsguy2707]

Nice! I hope the exam went well for you 🙏 Thanks for watching the video!

[@moonlight-cj2cv]

Yay I’m your 1000th subscriber 🥳

[@mymathsguy2707]

WooHoo!! Awesome! You are the special one :) Thank you very much for your support!

[@meeraravikrishna15]

so satisfying how neatly they write

[@mymathsguy2707]

HaHa of course! :)

[@TopassBakery]

Thank you so much! I was searching everywhere trying to find a guide about the nature table.

[@mymathsguy2707]

No problem, really glad that the video helped you out! Thanks for messaging, I appreciate that :)

[@chungjinjaan6796]

Thanks for the video sir !

[@mymathsguy2707]

You are welcome friend! Thanks for watching :)

[@roroC777]

@@mymathsguy2707 sir, do you have more videos of you solving more complex questions about derivatives?

[@mymathsguy2707]

@@roroC777 In KZbin I have a Calculus playlist which may contain some videos that will be useful to you. You can check it out here: kzbin.info/aero/PLBqdTAYDIIBWtcD-jSaEjMRcxKynTG8aA

[@mymathsguy2707]

@@roroC777 Also, I have an online Calculus 1 course which is a course in differentiation. You can enrol for one week for free here: my-maths-guy.teachable.com/p/calculus-1

[@mymathsguy2707]

@@roroC777 If there are any specific problems you'd like me to make a video about let me know and I may be able to help :)

[@Kunal-yg9fs]

Thank you so much sir !!! it really helped me a lot....keep making more videos.

[@mymathsguy2707]

You're welcome friend, I'm very glad it helped! :) Check back for regular new videos

[@Kunal-yg9fs]

Btw way sir where are you from?🤔 Im from India 🤗

[@mymathsguy2707]

An amazing country, which part are you in? India has a rich tradition in Math - ramanujan had a special mind! I am in Scotland

[@Kunal-yg9fs]

@@mymathsguy2707 Ohhh 😅 Great... Im from West Bengal sir...

[@mymathsguy2707]

@@Kunal-yg9fs Like Tagore. His books are on my list to read sometime :)

[@calebmakwiti4848]

Great

[@mymathsguy2707]

Thank you :)

[@abubakarumarusman7201]

I really appreciate this presentation, but how can I get local minimum or local maximum of a function. or you can help me with a guide lines on how to decide a function is local maximum or local minimum. thank you for your presentation

[@mymathsguy2707]

Hello :) Thanks for the comment and question. It's a two step process. Step 1 - find the local max or min point (take the derivative, set it equal to zero, and solve the equation). Step 2 - determine what types of point it is (either local max, local min, or point of inflection). To determine the type you can either use a nature table (which is like a mini sketch of the graph) or you can use the second derivative test. I explain both methods in the video. Let me know if you have any further question, thanks, Gary

[@atopimechele4406]

You are so wow

[@mymathsguy2707]

:) Thank you, this is really nice feedback! I'm glad the video was useful to you

[@elizabethajayi9246]

How did you get 0 as the derivative for 0 and 2 from the nature table?

[@mymathsguy2707]

Elizabeth, it's because those are the x co-ordinates of the stationary points and it's always the case that at the stationary points the derivative equals 0. So you don't have to calculate these like the other numbers in the nature table - you can just write them in. Thanks for the question, hope that helps. Gary

[@elizabethajayi9246]

@@mymathsguy2707 thank you so much I get it now.

[@beau_mobile]

What if the equation you get after differentiating doesn't factorise?

[@mymathsguy2707]

Good question. Generally questions of this type would be designed so that the equation does factorise - so it could indicate either a mistake in the working or a ‘broken’ question. That said, it could just be a tough question where you need to solve the equation by some other means - for example, if the equation was quadratic you might have to solve it using the quadratic formula rather than factoring … that is possible 👍🏼

[@joshuaakintemi5396]

Is stationary point the same as turning point?

[@mymathsguy2707]

A turning point is a type of stationary point. There are three types of stationary point - a maximum turning point, a minimum turning point or a point of inflection. In fact there are two types of point of inflection - a rising one and a falling one. Essentially stationary points are where the graph of the function changes direction. Hope that helps 🙂

[@innocentkitangwakalenga8383]

teacher can you please help me with this question 6a2-ab-b2 those 2 they are powers. Factorise completely.

[@mymathsguy2707]

Like this my friend (3a + b)(2a - b)

[@innocentkitangwakalenga8383]

@@mymathsguy2707 thanks teacher but if it is possible can you make a video for me? please

[@mymathsguy2707]

@@innocentkitangwakalenga8383 A video to explain this problem or for something different?

[@innocentkitangwakalenga8383]

@@mymathsguy2707 yes sir so that i can know how to explain it.

[@mymathsguy2707]

I'll try to find some time to make a quick video for you soon :)

[@PeihanWu]

realy helpful! love you sir❥(^_-)

[@mymathsguy2707]

Awesome, you're very welcome! :)

[@furejul7619]

are you irish

[@mymathsguy2707]

Close, I'm from Scotland. Thanks for watching the video.

[@ursulauasutirua3862]

thank you sir

[@mymathsguy2707]

You’re welcome :) Thanks for watching!