Stage 36 · Limits, Derivatives & Their Applications

36.2.5 Instant Speed: Our First Application

36.2 How Fast Things Change: From Average to Instant

Point 5 of 5

36.2.5 Instant Speed: Our First Application

Core idea

The number on the speedometer at one instant is just position differentiated with respect to time, s′(t).

Module goal. Use a limit to squeeze "the average pace over a stretch" down into "the pace at this very instant," leading naturally to the heart of the derivative.
eastmath.com · 36.2 How Fast Things Change: From Average to Instant · 36.2.5 Instant Speed: Our First Application