The average rate of change is also known as the slope. If we are looking to find the average rate of change between x = -1 and x = 2, in order to find the slope between those 2 x values, we need the y's that go along with them. Fill in -1 for x in the function and solve for y: [tex] (-1)^3-3(-1)^2-(-1)+3=0 [/tex]. That means that the coordinate is (-1, 0). Fill in 2 for x in the function and solve for y: [tex] (2)^3-3(2)^2-(2)+3=-3 [/tex]. The coordinate there is (2, -3). Now we can set up the slope formula to find the average rate of change between those 2 points: [tex] \frac{-3-0}{2-(-1)}=\frac{-3}{3}=-1 [/tex]. Therefore, the average rate of change between x = -1 and x = 2 is -1
