Answer:
-2
Step-by-step explanation:
The average rate of change over [a, b] is simply the slope of the function over [a, b] because:
[tex]let\:g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a} = \frac{f(b)-f(a)}{b-a}[/tex]
We have to find the avg ROC over [-3, 1] so the slope over the interval is
[tex]\frac{f(1)-f(-3)}{1-(-3)} = \frac{-6 - 2}{4} = \frac{-8}{4} = -2[/tex]
