The average rate of change of a function over an interval is given by 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, the interval is −6≤x≤4, so a = -6 and b = 4. The function is h(x)=-x^2+x+4, so:
h(-6) = -(-6)^2 + (-6) + 4 = -20
h(4) = -(4)^2 + (4) + 4 = -8
Therefore, the average rate of change of h(x) over the interval −6≤x≤4 is:
Average rate of change = (h(4) - h(-6)) / (4 - (-6))
= (-8 - (-20)) / (4 + 6)
= 12 / 10
= 1.2
So the average rate of change of the function over this interval is 1.2.