InstantaneousRateof ChangeThe instantaneousrate of changeofx=f(t) at
the timet 0 is the slopemtanof the tangentline at the timet 0 on the graph.Example4:
Supposethat
- Find the averagerate of changeofywith respecttoxover the interval[0, 2].
- Find the instantaneousrate of changeofywith respecttoxat the point
Solution: - Applyingthe formulafor AverageRateof Changewith andx 0 = 0 andx 1 = 2 yields
This meansthat the averagerate of changeofyis 4 unitsper unit increaseinxover the interval[0, 2].