Rate of change vs. average rate of change of a functionWhat is the difference between the both? I am trying to find a separate definitions for both in a textbook, but it only defines average rate of change.I know that average rate of change is: c h a n g e i n y c h a n g e i n x But what is just rate of change then?

Question

Rate of change vs. average rate of change of a functionWhat is the difference between the both? I am trying to find a separate definitions for both in a textbook, but it only defines average rate of change.I know that average rate of change is:            c      h      a      n      g      e            i      n            y              c      h      a      n      g      e            i      n            x      But what is just rate of change then?

Kendrick Jacobs · Accepted Answer

The average rate of change is defined over some finite interval   Δ  x to be            Δ      y              Δ      x      The rate of change is the rate at which the function changes at one particular point and is found by taking the limit      lim          Δ      x      →      0                  Δ      y              Δ      x      Note that in the case of a linear function, y=mx+c, the rate of change and the average rate of change are identical (they both equal m).