Answer:
The average rate of change of the function over the interval is of 2.
Step-by-step explanation:
Suppose we have a function f(x), over an interval (a,b).
It's average rate of change over the interval is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]g(x) = x^2 + 10x + 19[/tex]
Over the interval -9 < x < 1, so [tex]a = -9, b = 1[/tex]. So
[tex]A = \frac{g(1) - g(-9)}{1 - (-9)} = \frac{g(1) - g(-9)}{10}[/tex]
We have that:
[tex]g(1) = 1^2 + 10(1) + 19 = 1 + 10 + 19 = 30[/tex]
[tex]g(-9) = (-9)^2 + 10(-9) + 19 = 81 - 90 + 19 = 10[/tex]
So
[tex]A = \frac{30 - 10}{10} = \frac{20}{10} = 2[/tex]
The average rate of change of the function over the interval is of 2.
