I'm currently enrolled in a calculus I course, we currently have an exam coming up in the next few weeks so I wanted to get some practice in before then. However, when I came across this problem I was stumped -- I'm not even sure how begin a problem like this. I understand that the "instantaneous rate of change" is basically synonymous for "find the derivative" but how do I go about finding the derivative if I don't have the points for R or S?
Link to the math problem and graph here
EDIT: Here is a live graph to show what I'm talking about here
$Q$ is on the graph, so you can write down an expression for the coordinates of $Q$. From that, you can find the equation of the line through $P$ and $Q$, and the location of the midpoint $S$ of the segment $PQ$, then the equation of the perpendicular bisector of $PQ$, then the coordinates of the point $R$, then the length of the segment $RS$. And having an equation for the length of $RS$ as a function of $x$, you know how to find the instantaneous rate of change.