FindinExtrema Local”

lyric © 2006, 2014  Lawrence Mark Lesser

(to tune of the Desmond Child & Robi Rosa song “Livin’ La Vida Loca” that was a #1 hit for Ricky Martin in 1999)

She’s into the dramatic, seeking extremes of all--

With graphs in mathematics, how curves will rise and fall.

She has a revelation, she knows now what to try

To get a good description-- f prime will be her guide.

She’ll take out her good pencil and she’ll draw a number line,

She’ll note where f prime’s zero or where f prime’s undefined,

And where it changes sign:      c’mon!

Plus then minus means maximum that is local;

Minus then plus means minimum that is local.

This point is critical, so c’mon, let’s get vocal!

When f prime swaps sign, findinextrema local,

Findinextrema local, findinextrema local!

Our book names that method the First De-riv’tive Test;

Another tool to confirm extrema is the second derivative:

If f prime prime is positive, you have a valley’s path;

If f prime prime is negative, you have a local max -- buddy, that’s the facts!

Local extrema could be extrema global,

But right now we’re just findinextrema local,

Findinextrema local, findinextrema local!