WORKSHEET:
Average Rate of Change versus Instantaneous Rate of Change

1. 1. Sketch the graph of $f(x) = x^2$, focusing attention on the interval from $0$ to $3$.
   2. Compute the average rate of change of $f$ on $[0,3]$.
   3. On your graph, clearly indicate a line whose slope is this average rate of change.
   4. Fill in the blanks with the words greater than or less than:
      The instantaneous rate of change of $f$ at $x = 0$ is ____________________ the average rate of change of $f$ on $[0,3]$.
      The instantaneous rate of change of $f$ at $x = 3$ is ____________________ the average rate of change of $f$ on $[0,3]$.
   5. Clearly indicate on your graph two lines, whose slopes are the instantaneous rates of change at $x = 0$ and $x = 3$.
   6. If the outputs from $f$ are measured in feet and the inputs are measured in seconds, then what are the units of the average rate of change? The instantaneous rate of change?
2. 1. Sketch the graph of $f(x) = x^2$, focusing attention on the interval from $-3$ to $0$.
   2. Compute the average rate of change of $f$ on $[-3,0]$.
   3. On your graph, clearly indicate a line whose slope is this average rate of change.
   4. Fill in the blanks with the words greater than or less than:
      The instantaneous rate of change of $f$ at $x = -3$ is ____________________ the average rate of change of $f$ on $[0,3]$.
      The instantaneous rate of change of $f$ at $x = 0$ is ____________________ the average rate of change of $f$ on $[0,3]$.
   5. Clearly indicate on your graph two lines, whose slopes are the instantaneous rates of change at $x = -3$ and $x = 0$.
   6. If the outputs from $f$ are measured in cubic feet and the inputs are measured in minutes, then what are the units of the average rate of change? The instantaneous rate of change?