How to find stationary points and determine the nature (Example 2) : ExamSolutions

Worked example of finding a stationary point through differentiation, and determining whether it is a maximum or minimum.
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[@erickasewecomedy8541]

Thanks you very much for saving my mathematics grade

[@bobbuilder22]

Thank you once again for saving my maths grade!!!

[@dragonazh8850]

I dont understand the nature table part. Why does the 30x turn to negative but the 60x not?

[@ahmadshumail731]

Ahad because x=-2 so 60 x (-2 x -2 x -2 x -2) = positive BUT for 30 x (-2 x -2 x -2 x -2 x -2) = negative Zat make sense?

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Don’t lie

[@jacklowndes9004]

Really needed this, I've got my A-level mocks in a couple of days and was struggling to get my head around stationary points, cheers

[@teatime9198]

Thank you so much for this tutorial, you've explained this so well and I've really understood this now! Thank you once more!!!

[@RM-ds2ex]

This was really helpful, thanks!!! I'd seen other videos but they had less complicated equations so it was good to see a more complex one done. I might just pass my exam now so thanks!! Also, you're a great teacher, really clear explanation.

[@ingeniumpregium2679]

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[@moguada]

thank you!! such a clear, straightforward no nonsense way to explain this :)

[@Jasonlimitless]

Teaching myself A level maths and your videos are so useful! Could you recommend a site or page for example questions or questions to practice your lessons?

[@maximusfantabulous2559]

Such an awesome explanation and the visuals really help. Thanks!

[@safxtn5768]

Crazy that it's been 11 years since he made this AMAZING video and he's still liking our comments. Legend.

[@ExamSolutions_Maths]

@thezohan2112 You could look at the gradient either side. I show this in other tutorials on stationary points. Have you seen them? Look on my index on the homepage of my website if not.

[@501supershine]

cleared my doubts, thank you very very much!!

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I haven't watched more helpful videos than these ones!! You have a very loyal fan indeed!

[@ExamSolutions_Maths]

Lize van Dyk Welcome.

[@Mr96Mal]

Thank you very much, that really helped!

[@loaybukr7644]

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[@mariehill6547]

Thank you for the video! Just a quick question, can you prove that a stationary point is the point of inflection when a small decrease/ increase in x means that dy/dx is positive on both sides? Thank you!

[@08Victa]

So much respect for you, sir.

[@frankezenwanne]

I really love this...Thanks

[@farris6691]

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[@ExamSolutions_Maths]

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Awesome explanation 🙌

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[@ExamSolutions_Maths]

Thanks.

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You should have corrected him and said you're* :'(

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savage

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[@no.4613]

your english teacher wasn't

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[@ExamSolutions_Maths]

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Great explanation

[@Alysmegsta]

This helped so much! Thank you!

[@ExamSolutions_Maths]

+Alys McCarthy That's good. I am pleased you found it helpful

[@ca11umsmith5]

Explained it better than our A-Level teacher in just a few minutes - and this is from 2010

[@travisfrancis5392]

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[@ExamSolutions_Maths]

That's good, thanks for watching, I hope it went well for you.

[@zamdwa7084]

@daniel bonello you factorize the x^4 out

[@mok8936]

Hi, Do I need to know both the differential methods or can I get away with just knowing one? Thanks

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My concepts were under attack; this video saved them.

[@kamarulariffin9286]

what is the apps for editing this video

[@savokisan]

one question. How did you determine the shape of the graph at last part ?

[@destinylegend8098]

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[@ExamSolutions_Maths]

Thanks for your support.

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Thanks so much for this. Your like my second tutor but free one. Thanks so much will be watching your other videos as well. You answered all of my questions in this video Thanks again

[@ExamSolutions_Maths]

+Rohit Pai (rodude123) Thank you for your comments. Any support you can give is always appreciated is you find these of benefit.

[@rohitdoestech]

You welcome

[@mariehill6547]

Just a random query, what is the most effective way to make notes for maths?

[@ffaiq]

THANK UUUU

[@ExamSolutions_Maths]

You cannot say with certainty that when d2y/dx2=0 that the point is a point of inflexion so yes refer to the table.

[@thezohan2112]

what would you do instead of the double differentiation??

[@aaronowusu5202]

Awesome

[@ACiDiC619]

you can use the fact that when d2y/dx2=0 and d3y/dx3 doesn't = 0 the stationary point is a point of inflexion?

[@JamBeauty]

hi i got a question to do but ive never done it with only two numbers...i hope you can help....here goes....what are the stationary points of this function x3 (cube)- 6x2(square)

[@bahlolrehman1503]

Hi peter, you are an amazing teacher. I wanted to ask that why do you put the value of the x cordinate in the second differential i.e dy2 divided by dx2.

[@ExamSolutions_Maths]

That is the point we are testing and d^2y / dx^2 gives the rate of change of gradient and from this (see previous tutorial) we can tell the nature of the stationary point.

[@bahlolrehman1503]

@@ExamSolutions_Maths Thank you.

[@MohamedSaad-ir5lj]

10 years later and the video is better than 2020 ones

[@Therealryu10]

can't you say that when d2y/dx2=0, the nature of the sationary point is that it's an inflexion, or is it always inconclusive and do you have to resort to the table

[@ahmadshumail731]

Legend

[@AM-pg6vy]

As you said instead of zero we can try to -2 but if we take the -3 on left side and -1 in right wont the value -3 out number the -2 which is out of range ?

[@ExamSolutions_Maths]

@wearemce2010 differentiate, equal it to zero, factorise and solve.

[@jacobwilson5584]

When you add x= -2 into d^2y/dx^2 it comes to -4320, did i do something wrong because this doesn't make sense!

[@georgeacres4]

at 6:29, with 60x^4 when x=-1, how does that equal 60? I got that it equals -60 because -1^4 is -1, and 60*-1 is -60. Please can you explain?

[@ExamSolutions_Maths]

-1 x -1 x -1 x -1 = 1 not -1. I suggest you think of it as (-1)(-1)(-1)(-1) especially if using a calculator

[@DannyMLT]

Hi , I also divided by 30 and was left with 2x^4 + x^5... how do you factorise from this ? Thanks for the vids If I pass my degree exam will deff be leaving a nice donation :)

[@ExamSolutions_Maths]

@allstarjai1010 You can do that.

[@ws10football5]

How did you get x as 0

[@phyusinmyint1752]

hi you are such a great teacher but for the first question I got -703, what did I do wrong

[@nadh3478]

Sorry.. can i know why we need to to make that table??

[@kingHD11]

This is fucking brilliant wow thank you

[@ryangoburdhone8149]

why does x = 0 when finding the second differential?

[@ExamSolutions_Maths]

+Ryan Goburdhone It was the point we found at 1:57.

[@monicaj7539]

What if one of the (x) is zero. What do you do then.. I learnt you got to work with (0.5) and (-0.5)?? Though I am abit unclear with this.

[@monicaj7539]

Pardon?

[@eliopalombi]

Monica J still waiting

[@Amanda-bg7ib]

If the second derivative = 0, then it is a point of inflection (meaning it changes from concave up to down or vice versa). The result is not inconclusive 4:56

[@ExamSolutions_Maths]

Sorry to say but it is until you do the table. If you were to have say y=x^4, dy/dx=4x^3 and when dy/dx=0, x=0, y=0, d2y/dx^2 = 12x^2 and when x=0, d2y/dx^2=0 but it is a min in this case not a point of inflexion.

[@ishebacornwall5885]

How did he get the 2 + x in the brackets?

[@z4inz]

He factorised it. You can just use a calculator for that.

[@Jasonlimitless]

While plotting the graph 'This is not to scale but I just want to illustrate a few points' Slipping sneaky calculus joke in there?

[@losblancos99]

At 8:30 I tried the 1 differienational method and got the point (-2,-63) as a maximum point. Help please!

[@WiseFoolTrades]

losblancos99 You probably did something wrong when using the first differential. I used the first differential method and I got (-2,-63) as a minimum point.

[@losblancos99]

Wise Fool Your comment is a bit late as I already did my exam two days ago but I'm fine now

[@WiseFoolTrades]

losblancos99 Haha well I have mine coming up on Wednesday!

[@losblancos99]

Yeah I got another Maths exam on that day too. I am doing C2 OCR

[@WiseFoolTrades]

losblancos99 I see. I'm retaking exams from my edexcel module.

[@zamdwa7084]

Can't u just say that when x=0 d2y/dx2 =0 and therefore it is a horizontal point of inflection?

[@wearemce2010]

how to find Stationary point F(x) = x^4 - 1/2x^2 +1

[@DavidBux101]

hey ive got a math test tomorrow wish me luck cya

[@ExamSolutions_Maths]

A bit late but I hope it went well.

[@anthonymezzatesta1365]

Callux? 🤔

[@linozapped6278]

I have my math methods test tomorrow wish me luck

[@ExamSolutions_Maths]

Best wishes Lino

[@ExamSolutions_Maths]

Not at all. For example take y=x^4. when x=0 it is a min

[@Jasmineliketheflower]

how does x^4 = 0 .sorry I don't understand

[@lacerav5818]

Jasmine liketheflower either 2+x is 0 or 30x^4 is 0 because the whole expression is 0 so anything times 0 is 0 so at least one of them has to be 0 for the expression to be equal to 0 so x^4 has to be 0 because 30 times 0 is 0 and that times 2+x is 0

[@chigozie2739]

Please why do you differentiate twice

[@Sxyel]

i am very sry but this made everything more complicated. Is there an easier way?

[@ACiDiC619]

can you*

[@RatonLSD]

thanks lmaoooooooooo ez 100

[@yamin_05]

i dont fucking understand anything you dont even explain you just do examples

[@shehlaamir6011]

because this is a example video. he has videos where he actually explains the concepts. you can watch them instead.