Answer the following questions about average rates of change.

1. For a general function $f(x)$, what does $\frac { f ( 5 ) - f ( 3 ) } { 5 - 3 }$ represent?

   Answer (a):

   The average rate of change of $f$ on the interval $[3,5]$.
   It is the slope of the line between those $2$ points.

2. If $f(x) = x^2 + 3x + 2$, find $\frac { f ( 5 ) - f ( 3 ) } { 5 - 3 }$.

   Step (b):

   $\frac{5^2+3(5)+2-(3^2+3(3)+2)}{5-3}$