Suppose the distance that Emil the hedgehog has rolled is given by the function f(r) = 2r2 + 7r + 10, where f (r) is in meters and r is in seconds.

Compute Emil’s average speed (average rate if change) between time r and r + ∆r. (To simplify entering functions we will use h for ∆r.)

This formula will help: f(r + h) – f(r)/h.

Emil’s average speed:

Now, compute Emil’s velocity (instantaneous rate of change) as a function of r.

What is Emil’s velocity at time r = 0?