# Cubics Proof

• May 1st 2006, 03:53 AM
classicstrings
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!
• May 1st 2006, 03:14 PM
ThePerfectHacker
Quote:

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 :eek:
• May 1st 2006, 10:54 PM
classicstrings
oops, i meant prove it for ax^3 + bx^2 + cx + d

sorrY!
• May 2nd 2006, 01:26 AM
JakeD
Quote:

Originally Posted by ThePerfectHacker
The curve, $y=x^3$ got no maxima nor minima :eek:

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. :)
• May 2nd 2006, 02:01 AM
CaptainBlack
Quote:

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