Exam Questions: www.1stclassmaths.com/_files/... 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.
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
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!
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
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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?
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.
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.
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.
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.
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🥲
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
