Answer
a) The points $A$ and $B$\\
b) The slope of the line passing through $A,B$ is greater than the instantaneous rate of change in $B$ (see graph)
c) See graph
Work Step by Step
a) The average rate of change of the function between two points is the slope between the two points.
We notice that the slope between the points $A$ and $B$ is the steepest, so the greatest average rate of change is between the points $A$ and $B$.
b) Join the points $A$ and $B$ to show the the average rate of change of the function between $A$ and $B$. Also draw the tangent to the graph in point $B$ to show the instantaneous rate of change at $B$.
We notice that the slope of line passing through $A$ and $B$ is greater than the slope of the tangent in $B$.
c) Draw a tangent line to the graph in $C$ and $D$ so that the slope of the tangent line is the same as the average rate of change of the function between $C$ and $D$.
