# Thread: Cubics Proof

1. ## Cubics Proof

Hi!

How would I prove that joining the maximum and mimimum of a cubic will form a line that always intersects the cubic at the middle of those two points? How do I prove it generally? Thanks!

2. Originally Posted by classicstrings
Hi!

How would I prove that joining the maximum and mimimum of a cubic will form a line that always intersects the cubic at the middle of those two points? How do I prove it generally? Thanks!
The curve, $y=x^3$ got no maxima nor minima

3. oops, i meant prove it for ax^3 + bx^2 + cx + d

sorrY!

4. Originally Posted by ThePerfectHacker
The curve, $y=x^3$ got no maxima nor minima
Based on this post on another site, the proof will use the local max and min. It's interesting there's nothing there about the global max/min issue.

5. Originally Posted by JakeD
Based on this post on another site, the proof will use the local max and min. It's interesting there's nothing there about the global max/min issue.
PH's point is that $y=x^3$ does not have local extrema.

RonL