Rates of Change

You drive 120 miles in 2 hours. Your average speed was 60 mph — but you certainly weren't driving exactly 60 at every instant. You sped up, slowed down, stopped for coffee. The 60 mph is an AVERAGE rate of change: total distance divided by total time. It's the single steady speed that would have covered the same ground. This simple ratio — rise over run between two points — is the seed from which all of calculus grows.