I Turned Derivatives Into Music (x², x³, x⁴)

What does a derivative sound like?
The bottom graph is the slope of the top one, drawn as a music staff. Every time the slope crosses a line, that note plays.
x² has a straight-line slope, so it plays a clean rising scale.
x³ − 3x has a U-shaped slope: down the scale, then back up.
x⁴ − 2x² has a wavy slope that keeps returning to the same note.
That note is D, and it means slope = 0. Each time a curve hits a flat spot, the bell rings: once for the parabola, twice for the cubic, three times for the quartic. A degree-n polynomial can have at most n − 1 flat spots.