I didn’t read the OP closely enough. I thought the extrema were given as ordered pairs. If it is just the x values then you are right, it doesn’t matter.
ETA: if n doesn’t matter and i, j and k are integers then I would pick n=12 to make everything clean. Also, the sign flip comes because 2 maxima and 1 minimum means the quartic is concave down so a must be negative.
Well, I’m not right. The guys upthread who told me that are right! That was my primary area of confusion when I started this whole process out.
It’s not fair that LSLGuy gets to be smart in calculus and fly F-16s and 747s.
Ah!
I’m not that smart in calculus. I did have a math minor as an undergrad, but that was damn near 40 years ago.
What I can do for some folks sometimes on some topics is bridge the gap between the true experts speaking and the folks who can’t articulate a clear question or recognize their own implicit assumptions. In other words I like to think I’m good at arm-waving level explanations with lots of simplifying assumptions.
You’ll notice of the two very small points I added here, one was promptly (and rightly) dissected & declared wrong by the true expert: the eminently distinguished & highly esteemed (but thoroughly mis-named) indistinguishable.
I’ve never flown a 747 and the odds are very, very small I ever will. So thanks for the kind words, and I know you mean well, but you’re 1 for 3 this time. And even the F16s were now over 25 years ago.
One suddenly feels old. It’s past my bedtime; off to enjoy my fiber supplement & prepare for bed.