true or false? (1 Viewer)

[B1andB2]

Hii,
Can someone please explain to me whether this statement is true or false, it's messing around with my brain LOL ( i think it's false but don't know the exact reason)

"The coordinates of the point of inflexion can be found by taking the average of the coordinates of the max and min turning points"

thank uuu

 

[#RoadTo31Atar]

I think it's false because to find points of inflexion you have to double differentiate.

 

[DnaRna]

False probably, what if either one of the min or max turning point is wider.

 

[Trebla]

It’s false. An obvious counterexample is if there was a discontinuity/asymptote at the middle of the two turning points (e.g. y = x + 1/x).

 

[tito981]

this will only work with polynomials with degree 3 or greater.

 

[Canteen]

I vaguely remember this being a property of cubic polynomials with three distinct roots....
I think its because the vertex of a parabola (the first derivative) occurs at an x value which is the average of the x intercepts (which will correspond to the max and mins on the cubic). As the vertex of a parabola will occur at a point where the second derivative of the cubic is zero (i.e. the inflexion point), the inflexion point will occur at the average of the max and min.
That's quite a wordy explanation though. Mathematically its quite simple to derive.