WORKSHEET:
Average Rate of Change versus Instantaneous Rate of Change

 Sketch the graph of $f(x) = x^2$, focusing attention on the interval from $0$ to $3$.
 Compute the average rate of change of $f$ on $[0,3]$.
 On your graph, clearly indicate a line whose slope is this average rate of change.
 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 $[0,3]$.
 Clearly indicate on your graph two lines, whose slopes are the instantaneous rates of change
at $x = 0$ and $x = 3$.
 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?

 Sketch the graph of $f(x) = x^2$, focusing attention on the interval from $3$ to $0$.
 Compute the average rate of change of $f$ on $[3,0]$.
 On your graph, clearly indicate a line whose slope is this average rate of change.
 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 $[0,3]$.
 Clearly indicate on your graph two lines, whose slopes are the instantaneous rates of change
at $x = 3$ and $x = 0$.
 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?