Given the function h, of, x, equals, x, squared, plus, 7, x, plus, 9h(x)=x
2
+7x+9, determine the average rate of change of the function over the interval minus, 9, is less than or equal to, x, is less than or equal to, 0−9≤x≤0.
To find the average rate of change of the function over the interval [-9,0], we first need to find the values of the function at x=-9 and x=0.
When x=-9:
h(-9) = (-9)^2 + 7(-9) + 9 = 81 - 63 + 9 = 27
When x=0:
h(0) = (0)^2 + 7(0) + 9 = 0 + 0 + 9 = 9
Next, we can calculate the average rate of change using the formula:
Average Rate of Change = (h(0) - h(-9)) / (0 - (-9))
= (9 - 27) / 9
= -18 / 9
= -2
Therefore, the average rate of change of the function over the interval [-9,0] is -2.