To find the average rate of change of the function f(x)=x²+x+2 over the interval [-2, 0], we can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where 'a' and 'b' are the endpoints of the interval.
In this case, a = -2 and b = 0. Let's plug these values into the formula and calculate:
f(-2) = (-2)² + (-2) + 2 = 4 - 2 + 2 = 4
f(0) = 0² + 0 + 2 = 0 + 0 + 2 = 2
Now, substitute these values back into the formula:
Average rate of change = (f(0) - f(-2)) / (0 - (-2)) = (2 - 4) / (0 + 2) = (-2) / 2 = -1
Therefore, the average rate of change of the function f(x)=x²+x+2 over the interval [-2, 0] is -1.
This means that on average, the function decreases by 1 unit for every 1 unit increase in x over the interval [-2, 0].