To start, calculate your endpoints of your interval. Do this by plugging in your limits on x, -1 and 1, into your function. This gives you f(-1)=(-1)^2-(-1)-1=1+1-1=1 and f(1)=1^2-1-1=-1. Now, use your two endpoints, (-1,1) and (1,-1), and use the formula for slope, [tex]m= \frac{y_2-y_1}{x_2-x_1} [/tex]. This gives you [tex]m= \frac{-1-1}{1-(-1)} = \frac{-2}{2} =-1[/tex]. This means your average rate of change is -1.
