Exam Questions: www.1stclassma... In this video I explain how to find stationary points and determine their nature. This video is intended for those studying AQA's Level 2 Further Maths GCSE.
Пікірлер: 78
@Honeybeescrochet3 ай бұрын
Good luck to everyone who has the exam tomorrow!!! Youre going to do great!
@sumayyahkhan88973 ай бұрын
Help I didnt know anything at the beginning of today I never attended any of my further maths lessons 😢
@deedoo29253 ай бұрын
@@sumayyahkhan8897good luck o7
@EthanShaw-ym2zi3 ай бұрын
thanks mate
@deqohanshi11403 ай бұрын
THANK YOU SO MUCH!
@Thishandleisalreadynottaken3 ай бұрын
Thank you!
@DARSHPATIL-d7s3 ай бұрын
I jus wanna thank you brother u have jus explained me the entire concept in 8 mins where my teacher takes 40 mins U are very efficient 😢❤❤
@1stClassMaths3 ай бұрын
You are most welcome
@crjaipal1303 Жыл бұрын
Finally all my doubts got cleared with the help of this video. thankyou so much sir
@mittalpadhiyar6118Ай бұрын
My anxiety after understanding this whole concept 📉,it was crystal clear,thankyouu!
@devanshimoliya44473 ай бұрын
Thank you so muchhh .... It really helped me to understand.... I thought that this topic was hard to understand but you just made it a lott simple and easy to understand!!!!! ☺☺☺☺
@1stClassMaths3 ай бұрын
You're welcome!
@moniquegeorge86396 ай бұрын
my factoring skills are trash, I'm mixing up the signs a lot
@mishaagarwal2565Ай бұрын
No one cares to explain in such detail , they just tell how to go about the process and how to get the answer!
@kebabz58566 ай бұрын
6:38 can you tell me how you got -1/x^2 when differentiating x^-1 plz
@1stClassMaths6 ай бұрын
Multiply by -1 so we have -x but reduce the power from -1 to -2 so it is -X^-2 but due to negative indices x^-2 = 1/x^2
@MaureenSitali5 ай бұрын
Yes power rule and laws of indices combined.
@SrideviGadual2 ай бұрын
Sir , i kindly request please explain the step 3xsquare -12x +9=0 to xsquare-4x+3=0 to( x-1)(x-3)=0 . Please explain these three steps sir 🙏🏻
@1stClassMaths2 ай бұрын
You want to look up factorising quadratic expressions. I haven't got a video on this yet but I will one day :)
@SrideviGadual2 ай бұрын
@@1stClassMaths thanks sir 🙏🏻
@snowwhite2038Ай бұрын
You just split (-12) into such a way that when added it gives (-12) and when multiplied it gives the product of 3 and 9. This is called factorisation. We split 12 into -9 and -3. Now adding these both will give the number that we split i.e., -12 and when multiplied we get 27. The new equation would be 3x² - 9x -3x + 9 = 0. Let's simplify it by dividing LHS and RHS by 3. So we got x² - 3x - x + 3 = 0. Let's take x² -3x and make it x(x-3) by taking common x out. Now let's so the same with -x + 3 , making it -1 ( x-3). Now remember our aim to do this was to make the contents of both the brackets same, which we did. So the final equation would be, (X-1) (X-3) = 0. Thus putting each bracket equal to 0 we got x=1 and x=3.
@NaitikSingh-xf2oc5 ай бұрын
Great content, keep it up
@1stClassMaths5 ай бұрын
Appreciate it!
@AvneeshPimpare-du8gp4 ай бұрын
Thank you sir
@ethaniellim-yq1kk3 ай бұрын
thank uuuu
@mutilatette Жыл бұрын
it’s the night before the exam and you’re saving my life like jesus THANK YOU SO MUCH.
@1stClassMaths Жыл бұрын
Good luck!!
@mutilatette Жыл бұрын
@@1stClassMathsI GOT AN 8 THANK YOU SO MUCHHH
@articticcblu11 ай бұрын
@@mutilatettenicee❤
@articticcblu11 ай бұрын
@@mutilatettewas that further maths
@swathimrunalini15875 ай бұрын
Thank u btw Jai shree ram
@KinexxRL Жыл бұрын
I just want to say I really appreciate your hard work in helping us with the exams. Your content is informative,very well explained and captivating . On behalf of all my classmates thank you
@1stClassMaths Жыл бұрын
It's my pleasure! Good luck tomorrow.
@lengmandanlol Жыл бұрын
THE CARRY of 1stclass maths getting me that 9
@1stClassMaths Жыл бұрын
GL
@UAMinheritator Жыл бұрын
Stationary points came up today as a 5 marker. We didn't go over stationary points in any detail in school, but thanks to your videos on differentiation, i was able to do the question incredibly easily. Thank you again for these great videos!
@1stClassMaths Жыл бұрын
That is awesome!
@siddhisolanki52163 ай бұрын
your expalanaion is too good
@vinamramishra715710 ай бұрын
Thanks!
@MaureenSitali5 ай бұрын
dy/dx of negative power gives negative power since you subtract 1 to the power and multiply base by the original power e.g x^-1: drop -1 to have -1x and subtract 1 from -1 to get power -2 combining the two the full derivative is -1x^-2 giving you -1 multiplying x^-2 or -1/x^2. I used power rule and laws of indices to write negative power x^-2 to positive power x^2
@lenagalyo70593 ай бұрын
literal legend
@AnjumSyed-ks3xe3 ай бұрын
Thank you so much 😊it made my topic crystal clear✨
@1stClassMaths3 ай бұрын
Glad it helped!
@Vishwesh555Ай бұрын
Sir superb explanation🎉🎉🎉
@ferrariamarela Жыл бұрын
What if the second derivative is equal 0? is it a maxima or minima?
@1stClassMaths Жыл бұрын
Great question. In this situation more investigation is needed. It could be either or also a point of inflection. This is not needed for this course though so I have not covered it in this video.
@premanandapatel40425 ай бұрын
Neither maxima nor minima
@1stClassMaths5 ай бұрын
@@premanandapatel4042 incorrect it could still be either.
@arlo23217 күн бұрын
You've gotta go forward for the 3rd and 4th order derivatives for that @@premanandapatel4042
@randomuser21833 ай бұрын
Great explanation but i have a question, What if there are more than 2 stationary points, suppose i have to find maxima and i get three values of x for which first derivative is equal to zero, and for two values of x, second derivative is negative. Then how do i find on which value of x would there be maxima? Do i have to put both of these value in original function to check which one gives greater value, or is there any other way to know?
@randomuser21833 ай бұрын
Like the example you gave in starting of video at 0:34
@1stClassMaths3 ай бұрын
Hi. You can have multiple maxima and minima. When we say "maxima" we are talking about a localised maximum point rather than the maximum for the entire function/graph. So the maxima is just where the graph reachs a peak then comes back down again but this could happen multiple times. E.g. the sin/cos graphs have infinitely many maxima and minima.
@STEMchannels3 ай бұрын
This video was so helpful. Thank you so much
@zanonoza49185 ай бұрын
A very helpful video . Thank you. I've just subscribed .
@1stClassMaths5 ай бұрын
Awesome, thank you!
@Vishwajeetkumar-pv2lb5 ай бұрын
what to do when 2nd derivative is equals to Zero?
@1stClassMaths5 ай бұрын
This is not needed for this course but is at A-Level. If it is 0 you need to check the gradient either side of the point as it max be either or a point of inflection.
@MaureenSitali5 ай бұрын
derivative=0 is inflection point
@1stClassMaths5 ай бұрын
This is not correct I am afraid. I assume you're referring to the second derivative but this is also not correct. For example if y = x^4 then the second derivative is equal to 0 when x = 0 but this is a minimum point. If the second derivative is 0 then it *could* be an inflection point but it not guaranteed. Furthermore inflection points do not have to be stationary points.
@mahdi-hasan7 ай бұрын
Thank you. It clearly explains the whole concept.
@1stClassMaths7 ай бұрын
You are welcome!
@Sara-mi4hq Жыл бұрын
Thank you!
@1stClassMaths Жыл бұрын
You're welcome!
@Sara-mi4hq Жыл бұрын
@@1stClassMaths The exam went really good thanks to you :)
@1stClassMaths Жыл бұрын
Excellent!!
@thebest-vt1gh Жыл бұрын
i am so confused in skl we got taught that you only find the first derivative and find out the stationary point then calculate the gradient before and after the stationary point to determine the nature but here it says to find the second derivative . do both ways work or no ? pls help me🥲
@1stClassMaths Жыл бұрын
Hi. The method you have been told is a valid way of checking for the nature of points but perhaps lacks rigour compared to using the second derivative. It makes the assumption that between the values you select either side of the stationary point nothing crazy happens e.g. a discontinuity or another stationary point. The teaching guidance says for specfication point 4.7 states: "prove whether a point at which the gradient is zero is a maximum or minimum point using either increasing/decreasing functions or d^2y/dx^2" I think it would be worth learning this method as you will need to know what the second derivative is come A level maths, if you chose to do it. The other method will be absolutely fine for this exam though :D