It's also half way between the stationary points (if they exist).

Can I use #MathsToday for maths I did on my own in my office?

#MathsToday

TMannlovesmaths.bsky.socialOct 10, 2024 12:11pm

Consider a quadratic function f(x) Let m be the average of the roots then the point (m,f(m)) is a stationary point Cool! Now consider a cubic function g(x) Let n be the average of the roots Where is the point (n,g(n))? What do you notice?

Investigating the cubic case is lovely exercise for A-Level pupils. I wonder how A-Level teachers would know the result?

@susanwhitehouse.bsky.social will have something to say about this 😂

It's got to be a snake, particularly the Adder.

What happens if the shape is symmetrical but the mean is undefined (fat tails etc). Does a shape that extends infinitely have a centre of mass?

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Hoping this catches some more teachers before the week is up! Parallel Academy completely free for Year 7s and will complement any maths enrichment you already do! Very little for teachers to do, sign up below in minutes. parallel.org.uk?teachers#UKTeaching#UKMathsChat#mathstoday#UkEd

I like that this is xcos(x) in disguise!