Question

Help, thank you so much!

Answer 1

-2

Explanation:

The average rate of change over [a, b] is simply the slope of the function over [a, b] because:

`let\:g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a} = (f(b)-f(a))/(b-a)`

We have to find the avg ROC over [-3, 1] so the slope over the interval is

`(f(1)-f(-3))/(1-(-3)) = (-6 - 2)/(4) = (-8)/(4) = -2`